A  'M  ' 


The  University  of  Chicago 


The  Structure  of  the  Atom 

Par  I  — Recent  Work  on  the  Structure  of  the  Atom 

Part  II— The  Changes  of  Mass  and  Weight  Involved 
in  the  Formation  of  Complex  Atoms 

Part  III— The  Structure  of  Complex  Atoms*    The 
Hydrogen-Helium  System 


A  DISSERTATION 

SUBMITTED    TO    THE    FACULTY    OF    THE    OGDEN    GRADUATE 

SCHOOL  OF   SCIENCE   IN   CANDIDACY   FOR   THE 

DEGREE  OF  DOCTOR  OF  PHILOSOPHY 

(DEPARTMENT  OF  CHEMISTRY) 


By  Ernest  D.  Wilson 


A  Private  Edition 

Distributed  by 

The  University  of  Chicago  Libraries 
1916 


The  University  of  Chicago 


The  Structure  of  the  Atom 

Part  I— Recent  Work  on  the  Structure  of  the  Atom 

Part  II— The  Changes  of  Mass  and  Weight  Involved 
in  the  Formation  of  Complex  Atoms 

Part  HI— The  Structure  of  Complex  Atoms*    The 
Hydrogen— Helium  System 

A  DISSERTATION 

SUBMITTED    TO    THE    FACULTY    OF    THE    OGDEN    GRADUATE 

SCHOOL   OF  SCIENCE   IN   CANDIDACY  FOR  THE 

DEGREE  OF  DOCTOR  OF  PHILOSOPHY 

(DEPARTMENT  OF  CHEMISTRY) 


By  Ernest  D.  Wilson 


A  Private  Edition 

Distributed  by 

The  University  of  Chicago  Libraries 
1916 


BSCHENBACH    PRINTING    COMPANY 
E  ASTON,    PA. 


Part  I 
Recent  Work  on  the  Structure  of  the  "Atom 

When  Dalton1  advanced  his  atomic  theory  of  the  constitution  of  matter, 
he  thought  of  the  atom  as  the  ultimate  material  unit.  The  discovery  of 
the  phenomena  of  radioactivity,  however,  made  it  evident  that  this  view 
was  incorrect,  and  showed  that  the  atom  must  be  complex.  The  ques- 
tion of  its  structure  has  remained  unsolved  for  a  long  time,  and  it  is 
only  very  recently  that  there  has  been  any  experimental  work  upon 
which  to  base  a  theory.  In  this  paper  practically  all  of  the  important 
recent  work  bearing  on  this  subject  will  be  considered,  and,  wherever 
possible,  the  results  due  to  the  different  investigators  combined.  As 
the  results  often  seem  to  be  contradictory,  the  difficulty  of  reaching  any 
definite  conclusion  is  great. 

One  of  the  first  difficulties  which  arises  in  the  attempt  to  develop  an 
"atom  model"  is  the  fact  that  even  at  the  present  time  we  know  noth- 
ing of  the  nature  of  positive  electricity.  The  different  characteristics  of  the 
negative  electron  have  been  known  for  some  time,  but  the  question  of  a 
positive  electron  is  still  open. 

The  first  atom  model  was  suggested  by  Lord  Kelvin,1  and  consisted 
of  concentric  rings  of  rotating  negative  electrons  in  a  sphere  of  homo- 
geneous positive  electricity  the  size  of  the  atom.  This  model  has  come 
to  be  known  as  the  Thomson  atom,  due  to  the  fact  that  he  developed  it 
quite  completely,  and  worked  out  in  detail  the  number  of  electrons  in 
the  various  rings  necessary  to  give  stable  systems.  The  advantages 
of  this  construction  lie  in  the  relative  simplicity  of  the  mathematical 
calculation  of  the  distribution  and  velocities  of  the  electrons,  as  compared 
with  the  great  difficulties  involved  in  a  satisfactory  solution  of  such  prob- 
lems in  connection  with  the  later  atom  models.  Thomson  has  shown 
that  such  an  atom  imitates  to  a  large  extent  the  properties  of  our  known 
chemical  atoms  and  explains  why  some  are  electropositive,  others  elec- 
tronegative, and  the  variation  of  the  chemical  properties  with  the  atomic 
weight. 

One  objection  to  this  model,  which  also  applies  to  the  other  models  unless 
a  rather  questionable  assumption  is  made,  is  that  the  atoms  so  formed 
would  not  be  stable,  for  according  to  the  electromagnetic  theory,  elec- 
i  "On  Chemical  Synthesis,  from  a  New  System  of  Chemical  Philosophy,"  Man- 
chester, 1808,  pp.  2 1 1-6,  219-20. 


Irons  in  orbital  motion  must  radiate  energy,  and  hence  at  some  time  the 
atom  would  break  up. 

An  objection  that  is  even  more  important  is  that  the  positive  spheres 
of  Kelvin  would  have  an  electromagnetic  inertia  which  would  be  negligi- 
ble compared  with  that  of  even  a  single  negative  electron,  leaving  prac- 
tically all  of  the  mass  of  the  atom  unaccounted  for  on  this  theory. 

The  first  theory  of  the  constitution  of  the  atom  with  any  experimental 
work  as  a  basis  is  due  to  Rutherford.  He  made  use  of  the  phenomenon 
of  the  scattering  of  alpha  and  beta  particles  in  passing  through  matter.2 
The  deflection  is  more  marked  for  the  beta  than  for  the  alpha  particle, 
due  to  the  smaller  momentum  of  the  former.  There  seems  to  be  no 
doubt  that  the  particles  pass  through  atoms,  and  that  their  deflections 
are  due  to  the  intense  electric  field  within  the  atom.  Calculation  shows 
that  the  distribution  of  the  positive  electricity  assumed  in  the  Thomson 
atom  does  not  admit  of  sufficiently  strong  fields  to  deflect  an  alpha  parti- 
cle through  a  large  angle,  and  the  scattering  of  the  alpha  and  beta  rays  in 
passing  through  thin  sheets  of  metal  had  been  attributed  to  a  number 
of  small  scatterings.  Geiger  and  Marsden,3  working  with  gold  foil 
0.00004  cm-  thick,  found  that  about  i  in  20,000  alpha  particles  was  de- 
flected at  an  average  angle  of  90°.  Also,  Geiger4  showed  by  the  theory 
of  probabilities  that  the  most  probable  deflection  was  0.87°,  and  that  the 
chance  of  a  90°  deflection  was  vanishingly  small.  In  the  theory  of  the 
Thomson  atom  the  large  deflections  were  considered  as  due  to  the  accumu- 
lative effect  of  a  number  of  small  ones.  The  distribution  of  alpha  parti- 
cles deflected  through  large  angles  does  not  follow  the  probability  curve. 
Also,  after  one  collision  the  probability  of  the  same  ray  suffering  another 
in  such  a  way  as  to  give  a  larger  deflection  is  very  small. 

Considering  the  deflections  as  due  to  a  single  encounter  with  an  atom, 
Rutherford  has  obtained  an  expression  for  dm,  the  fraction  of  the  total 
number  of  alpha  particles  which  are  deviated  between  p  and  p  +  dp. 

dm  =  7T/4  ntb2  (cot  4/2  esc  0/2)  dp 

where  n  is  the  number  of  atoms  per  unit  volume,  t  the  thickness  of  the 
metal,  b  the  distance  from  the  center  to  which  an  alpha  particle  would 
penetrate  if  shot  directly  at  the  atom,  and  p  the  perpendicular  distance 
from  the  center  of  the  atom  to  the  extension  of  the  line  of  path  of  the 
approaching  alpha  particle.  Geiger5  has  shown  this  equation  to  be  true 
between  30°  and  150°. 

Thomson  considered  the  scattering  as  due  to  the  accumulative  effect 
of  a  number  of  small  scatterings,  and  obtained  the  following  expressions: 
The  average  deflection,  6t,  for  a  sheet  of  thickness  /  is  6t  =  371-6/8 
The  probability  pi  that  the  deflection  is  greater  than  (f>  is  pi  = 


Rutherford  shows  that  the  probability  pz  for  the  same  thing  based  on 
the  theory  of  a  single  scattering  is 

p2  =  !!"_  b2nt  cot2  -. 

4        l        __  * 

If  p2  =  0.5,  £1  =  0.24.    If  p2  =  O.I,  pi  =  0.0004. 

Thus  the  probability  on  Rutherford's  assumption  is  greater  than  that 
on  Thomson's.  Both  of  these  theories  are  developed  on  the  assump- 
tion that  the  forces  between  the  particles  are  electrical,  and  follow 
the  inverse  square  law.  Darwin  has  shown  that  this  is  the  only  law  of 
force  which  is  consistent  with  the  facts.* 

These  considerations  would  seem  to  indicate  that  the  large  deflections 
actually  found  must  be  due  to  a  single  encounter  with  an  atom,  and  in 
order  to  obtain  the  necessary  strength  of  field,  the  positive  charge  would 
have  to  be  concentrated  at  a  small  point  instead  of  being  evenly  distri- 
buted throughout  the  entire  volume  of  the  atom,  as  in  the  theory  of  Thom- 
son. The  negative  electrons  vibrate  around  this  positive  nucleus,  form- 
ing a  kind  of  miniature  solar  system.  This  is  the  type  of  atom  first  sug- 
gested by  Nagaoka.6  From  the  measured  deflections,  Rutherford  esti- 
mated that  the  charge  on  the  nucleus  was  approximately  equal  to  one-half 
the  atomic  weight  of  the  element  times  the  electronic  charge.  The  large 
deflections  are  due  to  the  alpha  particle  passing  very  close  to  the  nucleus. 

With  beta  rays  the  effects  are  slightly  different,  for  since  the  force  is 
attractive  they  increase  speed  on  approaching  the  atom.  By  ordinary  elec- 
trodynamics this  involves  a  loss  of  energy  by  radiation,  and  an  increase 
in  apparent  mass.  Darwin  showed  that  if  the  beta  particle  passed  very 
close  to  the  nucleus  it  would  describe  a  spiral,  and  eventually  fall  in. 
This  might  explain  the  disappearance  of  swift  beta  particles  in  their  passage 
through  matter. 

The  case  of  the  passage  of  the  alpha  particles  through  hydrogen  is  of 
particular  interest,7  for,  since  the  alpha  particle  is  heavier  than  the  hydro- 
gen atom,  the  recoil  due  to  the  close  approach  of  the  atom  and  the  parti- 
cle should  be  very  large.  It  was  shown  that,  as  a  result  of  a  collision, 
the  hydrogen  atom  should  attain  a  velocity  of  1.6  times,  and  hence  a 
range  of  about  four  times  that  of  the  alpha  particle  itself.  Marsden8 
actually  found  hydrogen  atoms  with  a  range  of  about  90  cm.  in  hydrogen 
in  which  the  alpha  particles  had  a  range  of  only  20  cm. 

From  the  data  on  the  scattering  of  the  alpha  rays  in  passing  through  a 

*  NOTE. — A  recent  paper  by  Hicks  takes  into  account  the  magnetic  forces  also, 
and  shows  that  their  effect  may  be  of  the  same  order  of  magnitude  as  that  of  the  electro- 
static forces  only.  Any  theory  which  is  complete  must  take  account  of  both.  Cal- 
culations based  on  only  one  would  seem  to  be  of  doubtful  reliability.  See  Hicks,  Phil. 
Mag.,  Jan.,  1915. 


gold  leaf,  it  is  possible  to  calculate  an  upper  limit  for  the  radius  of  the 
nucleus  of  the  gold  atom. 

Ne  =  charge  on  the  nucleus  (positive). 

R     =  the  radius  of  the  sphere  of  electric  action. 

Ne  =  the  value  of  the  negative  charge  surroundrng  the  nucleus. 

x      =  electric  force  at  a  distance  r  from  the  center. 

v      =  potential  force  at  a  distance  r  from  center. 

Then,  -  Ne  (1  -  ±)  and  „  -  Ne  (l-±  +  J^). 

m     =  mass  of  alpha  particle. 
u     =  velocity  of  alpha  particle. 
E     =  charge  on  the  alpha  particle. 

Let  the  alpha  particle  be  shot  directly  at  the  atom,  being  brought  to 
rest  at  a  distance  b  from  the  center.  Then 

V2mw2  =  NeE  (1/6  —  3/R  +  &2/2R3). 

If  N  is  assumed  to  be  100,  which  cannot  be  very  far  from  the  correct 
value  for  gold,  the  distance  6  for  an  alpha  particle  of  velocity  2 .09  X  io9 
cm.  per  second  is  found  to  be  3.4  X  io~12  cm.  This  gives  a  maximum 
value  for  the  radius  of  the  nucleus  of  the  gold  atom. 

DanviiP  has  made  a  similar  calculation  for  the  hydrogen  atom  and 
obtains  the  value  1.7  X  io~13  cm.  for  the  diameter.  This  is  smaller 
than  the  diameter  of  the  negative  electron,  which  is  ordinarily  given  as 
2.0  X  io~13  cm.  The  question  arises  as  to  whether  the  mass  of  this 
positive  nucleus  is  entirely  electromagnetic,  like  that  of  the  negative  elec- 
tron. The  electrical  mass  of  a  charged  body  is  2e2/$a,  where  e  is  the  charge, 
and  a  the  radius.  Using  this  formula  the  radius  of  the  positive  nucleus 
of  hydrogen  comes  out  to  be  1/1830  that  of  the  negative  electron. 
Rutherford9  suggests  that  it  is  probable  that  the  hydrogen  nucleus  is  the 
long  sought  positive  electron. 

Rutherford  has  shown  that  it  is  impossible  to  account  for  the  high  speed 
of  expulsion  of  some  of  the  alpha  and  beta  particles  if  they  come  from  a 
ring  of  atomic  radius.  They  must  come  from  a  point  very  close  to  the 
center,  which  suggests  that  they  are  shot  from  the  nucleus  of  the  atom. 

The  present  theory  of  the  constitution  of  the  atom  is  based  on  the  facts 
given  above.  Each  atom  of  matter  is  supposed  to  be  made  up  of  a  posi- 
tively charged  nucleus  around  which  rotate  the  negative  electrons.  In 
the  heavier  atoms  there  are  negative  electrons  in  the  nucleus  also.  The 
nucleus  is  the  seat  of  practically  all  of  the  mass  of  the  atom,  for  the  nega- 
tive electrons  contribute  very  little  mass.  Barkla,10  from  his  work  on 
the  passage  of  X-rays  through  matter,  suggested  that  the  charge  on  the 
nucleus  is  about  1/2  A0,  where  A  is  the  atomic  weight  of  the  element. 
Van  den  Broek,11  and  later  Bohr,12  suggested  that  the  number  of  units  of 


charge  is  Ne  where  N  is  the  number  of  the  element  when  the  elements 
are  arranged  in  order  of  increasing  atomic  weight,  or  what  is  now  called 
the  atomic  number. 

Moseley's13  work  on  the  X-ray  spectra  of  the  elements  is  very  important 
also,  in  helping  to  give  an  insight  into  the  constitution  of  the  atom.  Work- 
ing along  the  line  first  suggested  by  Laue,14  and  Bragg;15  Moseley,  and  Dar- 
win have  developed  an  experimental  method  for  determining  the  X-ray 
spectra  of  the  elements  by  reflection  from  crystal  surfaces.  When  an  ele- 
ment is  used  as  the  anticathode  in  an  X-ray  tube,  it  emits  a  character- 
istic radiation  of  a  frequency  roughly  1000  times  as  great  as  that  of  the 
visible  light  waves.  Each  element  is  characterized  by  two  different 
radiations  which  have  been  called  the  K  radiation  and  the  L  radiation.16 
The  K  radiation  is  composed  of  two  lines  which  Moseley  has  called  the 
a  line  and  the  $  line.  These  are  the  ones  used  the  most  by  him  for  pur- 
poses of  calculation.  The  L  radiation  is  not  nearly  as  penetrating  as  the 
K  radiation,  and  usually  consists  of  about  five  lines. 

Moseley  recorded  the  spectra  photographically,  instead  of  using  an  elec- 
troscope for  a  detector  as  did  Bragg,  and  he  examined  he  X-ray  spectra 
of  the  elements  from  aluminium  to  gold.  He  found  a  very  remarkable 
relationship  between  the  frequencies  of  the  lines  of  the  various  elements. 
In  going  from  one  element  to  the  next  higher  in  atomic  weight  there  was  a 
shift  of  the  two  lines  of  the  K  series  toward  the  violet.  That  is,  there  is 
a  change  in  the  frequency  of  the  spectrum  lines  with  a  change  of  the  ele- 
ment. Moreover  there  is  a  very  simple  relationship  between  these  fre- 
quencies. Thus  considering  the  a  line,  the  frequency  is  expressed  by 
the  formula 

v  =  K(N  —  i)2 

in  which  K  is  a  constant,  and  N  is  a  number  which  increases  by  one  in 
passing  from  one  element  to  the  next  higher  in  atomic  weight.  If  13  is 
chosen  for  the  value  of  N  for  aluminium,  and  a  corresponding  value  of 
K,  N  turns  out  to  tbe  the  atomic  number  of  the  elements.  Thus  N  deter- 
mines the  X-ray  spectrum  of  any  element.  Moseley  finds  that  between 
aluminium  and  gold  the  order  of  the  elements  according  to  N  is  the  same 
as  that  of  the  atomic  weights  except  where  the  latter  would  put  the  ele- 
ment out  of  place  in  the  periodic  table.  Moseley  finds  only  three  un- 
known elements  between  aluminium  and  gold. 

He  has  shown  that  neoytterbium  and  lutecium  exist,  but  that  Urbain's 
celtium  is  a  mixture.  According  to  his  system  thulium  I  and  thulium  II 
of  Welsbach  exist,  but  not  thulium  III.  A  homolog  of  Mn  between  Mo 
and  Ru  remains  to  be  found  as  does  another  element  between  Os  and  W. 

Moseley  concludes  that  the  number  N  is  the  charge  on  the  nucleus 
of  an  atom,  and  that  this  charge  increases  one  step  at  a  time  from  one  ele- 


8 

ment  to  the  next.  According  to  this  view  it  is  perfectly  possible 
to  have  two  elements  of  very  different  atomic  weight  that  have  the 
same  X-ray  spectrum,  providing  only  that  they  have  the  same  nuclear 
charge. 

Such  elements  would  also  be  identical  chemically,  and  so  far  as  is  known 
at  the  present  time  would  have  identical  spark  and  arc  spectra. 

This  seems  to  be  borne  out  by  the  fact  that  Aston,17  working  with 
J.  J.  Thomson,  found  two  neons  with  atomic  weights  20  and  22,  which 
are  otherwise  identical,  and  have  the  same  spectrum.  He  was  only  able 
to  separate  them  by  diffusion  methods,  which  depend  on  the  atomic  weight 
and  hence  upon  the  density.  Also  Russell  and  Ross,18  and  Hxner  and 
Haschek,19  working  with  a  strong  ionium  solution,  could  not  obtain  any 
spectrum  except  that  of  thorium,  of  which  ionium  is  an  isotope. 

This  theory  of  the  dependence  of  the  chemical  and  physical  properties 
of  the  elements  on  the  nuclear  charge  is  supported  by  recent  work  on 
the  radioactive  elements.  The  position  of  all  these  elements  in  the 
periodic  table  was  an  unsolved  problem  until  it  was  shown  that  two  or 
more  elements  could  occupy  the  same  place  in  the  table.  It  has  been 
supposed  for  some  time  that  certain  of  the  radio-elements  were  inseparable 
by  any  known  chemical  means.  Fajans,  Soddy,  and  others  make  this 
a  general  property  of  these  elements,  and  treat  each  as  the  chemical  ana- 
log of  one  or  the  other  of  the  known  elements.  Two  elements  which 
occupy  the  same  space  in  the  periodic  table  and  are  inseparable  by  ordi- 
nary chemical  means  have  been  called  "Isotopes"  by  Soddy. 

The  rule  advanced  by  Soddy,20  Fajans,21  and  others,  that  the  expul- 
sion of  an  alpha  particle  causes  the  element  to  shift  its  position  in  the 
periodic  table  two  places  to  the  left,  and  to  decrease  in  atomic  weight  by 
four  units  is  also  in  accord  with  the  theory  if  we  consider  that  the  alpha 
particle  comes  from  the  nucleus  of  the  atom.  Similarly  the  expulsion 
of  a  beta  particle,  which  is  a  negative  electron,  would  cause  the  element 
to  shift  its  position  in  the  table  one  place  to  the  right,  without  any  change 
of  mass.  In  this  case  the  positive  charge  on  the  nucleus  is  increased  by 
one  unit. 

In  radioactive  changes  the  expulsion  of  a  beta  particle,  which  evidently 
is  shot  out  of  the  nucleus,  as  is  shown  by  its  extremely  high  velocity, 
causes  the  element  to  move  one  group  to  the  right  in  the  periodic  table, 
which  means  an  increase  of  one  in  the  atomic  number.  From  this  it 
seems  evident  that  this  gives  a  proof,  at  least  for  the  radioactive  ele- 
ments, and  probably  in  the  case  of  all  lower  atomic  weight  elements,  that 
an  increase  of  one  in  the  atomic  number  means  an  increase  of  one  in  the 
positive  charge  on  the  nucleus.  It  seems  probable,  therefore,  that  the 
number  of  positive  charges  on  the  nucleus  is  equal  to  the  atomic  number. 


TABLE  I. 

Element.                                    Radiation.  Valence. 

Ur  I  ..................  «  6 

UrXi  .................  0  4 

UrX2  .....  :  ...........  0  5 

UrII  .................  «  6 

lo  ....................  «  4 

Ra  ...................  « 

RaEm  ................  «  ° 

Ra  A  .................  «  6 

RaB  .................  ft  4 

RaC  .................  0«  5 

/  \ 

Ra  C,  Ra  C,1  ...........  «  0 


\ 


Ra  D 0  4 

RaE 0 

RaF «  6 

Pb 4 

Element.2  At.  wt.  At.  no.  Element. 

UrI '38  1  UrX: -^  9O 

UrII 234} 

RaA 218)  RaB 214 

RaF arc/  *4  RaD 210  82 

Pb 206  J 

1  According  to  recent  work  by  Miss  Meitner  there  seems  to  be  considerable  doubt 
as  to  the  existence  of  RaC2. 

2  This  table  gives  only  the  isotopes  of  the  radium  series. 

The  work  of  Rutherford  and  Andrade22  serves  to  further  confirm  these 
views.  The  wave  length  of  the  soft  7  rays  from  Ra  B  was  determined, 
and  also  the  X-ray  spectrum  of  lead,  with  a  view  to  determine  the  atomic 
numbers  of  these  and  the  other  radioactive  elements.  Ra  B  and  lead 
were  found  to  have  the  same  atomic  number,  82,  as  they  gave  the  same 
X-ray  spectrum.  From  Table  I  it  is  seen  that  there  are  several  groups 
of  elements  having  the  same  atomic  number  but  with  different  atomic 
weights.  These  are  tabulated  at  the  bottom  of  Table  I. 

It  will  be  noted  that  the  atomic  weight  of  lead,  if  its  source  is  the  uran- 
ium series  of  elements,  should  be  206 . 18,  using  the  latest  value  of  the  atomic 
weight  of  uranium  as  238.18.     The  atomic  weight  of  lead  has  recently 
been  determined  by  Richards,23  who  obtained  the  value  207.15  for  ordi 
nary  lead,  not  radioactive.     In  analyzing  the  lead  from  a  large  number 
of   radioactive   minerals,   mostly   uranium,   he   obtained  values   varying 
from  206 . 4  to  the  ordinary  value,  207 . 15.     Soddy,24  working  with  thonun 
minerals,  obtained  the  value  208,  which  would  be  expected  if  the  end' 
of    the  thorium  series  is  also  lead.     More  recently  Soddy25  has  start 
a  more  extensive  investigation,  and  has  obtained  about  80  grams  of  lead 


10 

from  thorium  minerals.  He  finds  that  the  lead  has  a  higher  density  than 
the  ordinary  lead.  This  is  to  be  expected  if  the  atomic  volumes  of  the 
isotopes  are  the  same.  Richards  found  no  difference  between  the  spec- 
trum of  the  lead  of  low  atomic  weight  and  the  ordinary  lead,  but  Soddy 
claimed  to  have  found  at  least  one  line  in  the  new  material  which  was  not 
given  by  the  old.  In  some  work  as  yet  unpublished,  done  by  Aronberg 
working  with  Gale  and  Harkins  no  difference  was  found  between  the 
spectrum  of  some  lead  from  Carnotite  and  the  ordinary  lead,  although 
the  Zeeman  effect  was  also  investigated.  In  this  investigation  a  21 
foot  concave  grating  was  used,  and  the  wave  lengths  could  be  measured 
to  o.ooi  of  an  Angstrom. 

Lindemann*  shows  by  means  of  simple  thermodynamical  reasoning 
that  two  elements  of  different  atomic  weight  must  differ  either  in  their 
chemical  or  physical  properties.  Since  Soddy  has  shown  that  the  isotopic 
forms  of  lead  have  the  same  atomic  volumes,  and  also,  of  course,  the  same 
chemical  properties,  it  follows  that  the  forces  between  the  atoms,  and  there- 
for the  vapor  pressures  and  the  melting  points,  must  vary,  and  that 
Soddy's  lead  from  thorite  should  have  a  melting  point  i .  54  degrees  higher 
than  ordinary  lead.  Lindemann  concludes  that  the  forces  of  attraction 
and  repulsion  between  the  atoms  have  their  origin  in  the  nucleus,  while, 
as  is  generally  considered,  the  chemical  properties  and  the  radius  of  the 
atom  are  conditioned  by  the  external  electrons.  In  isotopes  the  forces 
of  attraction  and  repulsion  are  proportional  to  the  atomic  weight,  that  is, 
probably  to  the  number  of  positive  particles.  These  forces  are,  however, 
not  usually  additive,  but  are  so  only  in  isotopes,  so  the  nuclei  of  isotopes 
probably  differ  in  their  linear  dimensions,  but  not  at  all,  or  very  little, 
in  the  arrangement  of  the  particles. 

The  fact  that  a  particles  are  expelled  in  so  many  of  the  transformations 
seems  to  show  that  the  nucleus  is  composed,  in  part  at  least,  of  helium 
atoms.  The  energy  of  the  expulsion  of  the  alpha  particles  can  be  ac- 
counted for  by  their  passage  through  the  intense  electric  field  around  the 
nucleus.  The  primary  beta  particles  probably  arise  from  a  disturbance 
of  the  nucleus,  which  must  be  very  complex. 

The  general  facts  which  seem  to  be  proved  by  all  this  work  described 
above  are,  that  the  nucleus  is  a  fundamental  constant  of  matter,  and 
that  the  charge  on  the  nucleus  determines  the  character  of  the  element. 
The  atomic  weight  is  not  so  characteristic  as  the  atomic  number  or  the 
nuclear  charge.  The  atomic  weight  is  a  complex  function  of  the  number 
and  configuration  of  the  electrons.  Those  properties  of  matter  such  as 
gravitation  and  radioactivity,  which  are  entirely  beyond  our  control 
by  any  chemical  or  physical  agents,  are  functions  of  the  nucleus. 

*  Nature,  March  4,  1915. 


II 


Un  to  this  point,  beyond  the  fact  that  the  atom  is  a  sort  of  Saturnian 
system,  nothing  has  been  said  as  to  the  arrangement  of  the  electrons 
in  the  atom,  or  the  distribution  of  the  forces.     The  first  attempt  to  treat 
this  problem  as  one  of  mechanics,  and  to  give  a  definite  picture  of  the  ate 
was  made  by  Bohr.26     In  his  calculations,  Bohr  has  UsSflBi  atom  of  the 
Rutherford  type,  and  has  combined  with  the  classical  mechanics  Plane 
quantum  hypothesis.     While  Bohr's  work  has  been  severely  criticized, 
the  very  remarkable  results  he  was  able  to  obtain  with  hydrogen  alone 
make  it  worthy  of  careful  consideration.     Bohr's  success  lies  only  in  t 
consideration  of  atoms  with  one  vibrating  electron.     The  following  is  a 
simplified  form  of  his  analysis: 

Let    m       =  mass  of  the  electron. 
—  e       =    charge  of  the  electron. 
M      =  mass  of  nucleus. 
H        =  charge  on  nucleus. 
a        =  radius  of  ring  of  rotation  of  electrons. 
co        =  frequency  of  revolution  of  electrons. 
Then,    27rco    =  angular  velocity. 
The  kinetic  energy  of  an  electron  can  be  expressed  in  two  ways: 

Y2  w(27rcoa)2     or     XA  *E/a. 
The  work  necessary  to  remove  an  electron  from  its  orbit  to  a  position 

of  rest  at  co  is: 

e^/a  __  i/2  w(27rcoa)2  =  V*  (*E/a)  ••  W. 

Then 


2a  = 


According  to  Newtonian  mechanics,  the  energy  W  should  go  on  increas- 
ing as  energy  is  given  out  by  radiation,  until  the  orbit  gets  smaller  anc 
smaller  and  the  electron  falls  into  the  nucleus;   that  is,  "a  '  would 
crease  and  co  increase.     Here  Bohr  introduces  the  quantum  hypothesis. 
He  assumes  that  the  angular  momentum  of  the  electron  is  consta 
and  equal  to  rh/2^  where  r  is  an  integer,  and  h  is  Planck's   constant; 
that  is,  the  angular  momentum  of  the  electron  in  its  orbit  is 

27rWCOa2    =    W/7TCO    =    T/J/27T. 

This  prevents  continuous  variations  of  W,  a,  and  co. 
Then, 


2a  =  _ 

27T2W*E 

Much  of  the  criticism  of  Bohr's  work  is  directed  at  this  point  in  his 
analysis      The  idea  of  an  electron  undergoing  accelerated  motion  wit 
out  radiating  energy  is  difficult  to  accept.     There  is  also  difficulty  in  o 


12 


taining  any  satisfactory  physical  picture  of  the  process  by  which  light 
is  emitted  when  the  electron  changes  from  one  steady  state  of  vibration 
to  the  next,  as  described  below. 

In  a  neutral  hydrogen  atom  r  is  -equal  to  i.  If  this  value  is  substitu- 
ted in  the  second  equation,  the  value  for  the  diameter  of  the  hydrogen 
atom  is  obtained  as  i  .  i  X  io~8  cm.,  which  is  of  the  right  order  of  magni- 
tude. 

The  electron  radiates  energy  only  when  it  changes  from  one  steady  state 
of  vibration  to  another,  and  then  one  quantum  of  energy  is  released; 
that  is,  for  a  sudden  shrinkage  from  orbit  of  TZ  to  n,  there  must  be  a  loss 
of  energy  W  =  hv  where  v  is  the  frequency  of  the  radiation. 

27T 


h* 

In  the  case  of  hydrogen,  E  =  e.  We  can  then  calculate  the  value  of 
the  constant  27r2w£2E2//*3  which  is  equal  to  3.26  X  io15.  The  well- 
known  B  aimer  formula  for  the  series  of  lines  in  the  hyrogen  spectrum 
is  v  =  K  (i/T22  -  -  i/Ti2)  in  which  K  as  determined  by  experiment  is  3.29 
times  io15.  This  practical  identity  of  Bohr's  calculated  value  of  the 
Rydberg  constant  and  the  experimental  value  is  probably  the  greatest 
triumph  of  Bohr's  work. 

If  the  value  i  is  assigned  to  TZ,  and  a  series  of  values,  i,  2,  3,  etc., 
given  to  TI,  the  frequencies  of  a  series  of  lines  in  the  ultraviolet  are  de- 
termined. This  series  was  not  known  at  the  time  of  Bohr's  first  work, 
but  has  since  been  found  by  Lyman  of  Harvard.  (Not  published.) 
The  physical  picture  obtained  of  the  production  of  this  series  of  spectrum 
lines  is  as  follows: 


13 


N  represents  the  nucleus  of  the  atom.  The  rings  i,  2,  and  3  correspond 
to  the  orbits  of  the  electron  in  the  various  steady  states  of  motion.  When 
an  electron  falls  from  one  steady  state  to  the  next  one  of  smaller  radius 
of  vibration,  one  quantum  of  energy  is  liberated.  In  the  above  spectral 
series  all  the  lines  are  formed  by  electrons  falling  from-the  second  ring 
and  beyond  all  the  way  to  the  first  ring.  The  first  line  in  the  series  is 
due  to  an  electron  falling  from  the  second  to  the  first  ring;  the  second  line 
to  an  electron  falling  from  the  third  to  the  first  ring,  and  so  on. 

If  T2  =  2,  and  a  series  of  values  be  assigned  to  n,  the  ordinary  Balmer 
series  for  hydrogen  results.  For  r2  =  3,  there  results  an  infra-red  series 
predicted  by  Ritz,  and  later  discovered  by  Paschen.  This  model  does 
not  account  for  the  Pickering  series  of  lines  which  is  ordinarily  attributed 
to  hydrogen,  but  Bohr  shows  that  this  series  is  accounted  for  by  the  helium 

atom. 

Very  recently  another  confirmation  of  Bohr's  theory  has  been  given 
by  Evans27  in  his  work  on  the  spectra  of  hydrogen  and  helium.  Bohr's 
formula,  when  modified  so  as  to  take  account  of  the  mass  of  the  nucleus,  is 


.  . 

"  h*(m  +  M) 

This  makes  a  slight  change  in  the  value  of  the  constant  in  passing  from 
hydrogen  to  helium,  and  the  ordinary  Balmer  series  for  hydrogen,  which 
according  to  Bohr's  original  work  could  come  from  either  of  the  two 
elements,  is  found  to  be  slightly  different  for  the  one  than  for  the  other. 
Thus  it  became  very  important  to  investigate  carefully  the  spectra  of 
these  two  elements,  and  see  if  this  series  could  be  detected  in  helium, 
and  whether  the  slight  differences  just  spoken  of  existed.  Evans  was 
able  to  observe  the  first  few  members  of  this  series,  and  the  measured 
values  of  the  lines  are  very  close  to  the  theoretical. 

Bohr28  has  also  shown  that  if  the  principle  of  relativity  is  introduced, 
his  formula  takes  the  following  form,  which  accounts  for  some  of  the  ex- 
tremely small  errors  found  by  Evans. 

27rVE2mM/  i          i  \  [T        TrVEV^ 
=  w(m  +  M)  W  "  n2/  L  *» 

Helium  is  considered  to  have  a  charge  on  its  nucleus  of  2e,  or  E 
The  atom  with  one  positive  charge  has  one  vibrating  electron. 
following  formula  results  for  helium: 


=  K 


The  physical  interpretation  is  the  same  as  for   hydrogen.     For   various 
values  of  r2,  the  following  series  result: 

r2  =  i — Extreme  ultraviolet;  not  known. 

T2  =  2 — Extreme  ultraviolet;  not  known. 


r2  =  3 — Two  series,  as  r\  is  odd  or  even.  (The  lines  of  the  two  series 
alternate.)  These  series  were  observed  by  Fowler  in  mix- 
tures if  hydrogen  and  helium,  but  had  been  attributed  to 
hydrogen. 

r2  =  4 — The  lines  of  two  series,  alternating  as  n  is  odd  or  even. 
The  first  of  these  is  the  ordinary  B aimer  series,  which  evidently 
can  come  from  either  hydrogen  or  helium.  The  second  is  a 
series  which  was  observed  by  Pickering  in  the  star  f-Puppis, 
and  was  attributed  to  hydrogen. 

In  the  work  of  Evans  which  was  mentioned,  there  is  a  further  confirma- 
tion of  Bohr's  theory.  By  carefully  adjusting  conditions  he  was  able 
to  obtain  the  Pickering  series  of  lines  from  absolutely  pure  helium,  which 
should  be  the  source  of  them,  according  to  Bohr. 

Balmer's  series  has  never  been  observed  in  the  laboratory  beyond 
r2  =  12,  while  in  stellar  spectra  it  extends  to  r2  =  33.  Therefore  in 
vacuum  tubes  no  hydrogen  atoms  exist  of  greater  diameter  than  corre- 
sponds to  r2  =  12,  or  2a  =  1.6  X  io~6  cm.  For  r2  =  33,  2a  =  i  .2  X 
io~5  cm.  Therefore,  according  to  Bohr's  theory,  there  are  in  the  stars 
hydrogen  atoms  1000  times  the  diameter  of  those  on  the  earth. 

Jeans31  points  out  that  in  the  above  work  the  value  of  M  is  supposed  to 
be  very  great  in  comparison  with  m.  If  this  is  not  true,  the  value  of 
Rydberg's  constant  is  given  by 

_   27T2£2E2  WM 

h*        (m  +  M)' 
If  M  refers  to  the  value  for  hydrogen,  2M  is  the  value  for  helium. 

Then  KH  '  KH«  =  -...     From  the  best  observed  value 

M  +  l/2m     m  +  M 

of  the  ratio  KH/KHg,  M/m  is  given  as  1836  =t  12,  which  is  in  close  agree- 
ment with  the  experimental  value. 

The  above  calculation  would  seem  to  be  inconsistent  with  the  idea 
of  the  atom  as  developed  by  Rutherford,  for  he  states  that  practically 
all  of  the  mass  of  the  atom  lies  in  the  nucleus.  In  that  case,  the  value 
of  M  for  helium  would  not  be  twice  but  four  times  the  value  for  hydrogen, 
and  the  helium  nucleus  would  consist  of  four  positive  and  two  negative 
electrons. 

Bohr  extends  his  calculations  to  the  lithium  atom,  and  in  considering 
only  one  vibrating  electron  obtains  good  results.  In  all  of  his  work, 
however,  when  more  than  one  electron  is  considered,  his  results  are  not 
correct.  One  of  the  serious  objections  to  Bohr's  theory  is  that  he  has 
been  unable  to  explain  the  ordinary  spectrum  of  hydrogen.  Nicholson22 
has  extended  Bohr's  calculations  to  every  possible  mode  of  vibration  in 
attempting  to  secure  a  formula  or  formulas,  giving  the  lines  of  the  ordinary 


15 

hydrogen  spectrum,  but  has  found  that  they  can  be  accounted  for  by  no 
possible  vibration. 

Perhaps  the  most  fundamental  objection  to  Bohr's  work  lies  in  the 
fact  that  he  has  combined  two  basically  different  kinds  of  mathematics 
in  working  out  this  theory.  It  might  be  possible  undersoch- conditions 
to  obtain  results  which  are  absolutely  incorrect,  for  the  two  are  contra- 
dictory. 

Nicholson  claims  to  have  proven  both  by  the  classical  mechanics  and  by 
Bohr's  mechanics  that  coplanar,  concentric  rings  of  vibrating  electrons 
are  unstable.  That  is,  if  there  are  to  be  two  or  more  rings  of  electrons 
in  an  atom,  they  cannot  lie  in  the  same  plane,  which  would  make  Bohr's 
theory  untenable.  This  presents  difficulties  in  still  another  way.  If 
we  consider  valence  as  due  to  certain  electrons  which  are  ordinarily  con- 
sidered as  being  near  the  outside  of  the  atom,  these  electrons  would  either 
have  to  be  in  an  outer  ring,  by  themselves,  or  else  have  some  peculiar 
properties  different  from  the  other  electrons  in  the  ring.  J.  J.  Thomsen 
not  only  believes  in  the  existence  of  more  than  one  ring  of  electrons,  but 
is  some  work  yet  unpublished,  states  that  he  has  actually  counted  the 
number  of  rings  in  certain  atoms.  This  claim  of  Nicholson's  would  seem 
to  be  wrong,  but  it  may  be  very  true,  as  he  says,  that  a  large  num- 
ber of  the  vibrations  in  such  a  system  are  unsteady,  and  would  result 
in  the  expulsion  of  an  electron.  < 

Bohr  has  not  had  better  success  in  accounting  for  a  large  part  of  the 
spectrum  of  helium  than  he  had  in  the  case  of  hydrogen.  Helium  has  six 
Balmer  series  which  are  not  explained.  Bohr  considered  only  the  first 
electron  in  his  calculations  on  this  element,  and  Nicholson  thought  that 
possibly  the  rest  of  the  spectrum  might  be  due  to  the  other  electron. 
He  therefore  made  the  necessary  calculations,  but  could  obtain  no  other 
series.  Two  of  the  series  of  lines  calculated  for  helium  lie  in  the  ultra- 
violet, and  are  not  knowm.  Lyman  of  Harvard,  as  a  result  of  his  inves- 
tigations, states  that  helium  has  no  Schumann  region  spectrum. 

It  is  well  to  remember  that  Bohr  attempts  no  physical  picture  or  cause 
of  the  change  of  an  electron  from  one  steady  state  of  vibration  to  the 
next.  In  his  theory  of  spectra,  the  energy  which  goes  into  the  spectrum  is 
atomic  energy.  This  would  be  a  serious  objection  if  it  were  not  for  the 
fact  that  it  is  very  easy  to  think  of  it  in  a  slightly  different  way.  The 
energy  which  it  is  necessary  to  apply  to  hydrogen  to  give  these  spectral 
lines  may  be  used  to  remove  an  electron  from  one  of  the  inner  rings  of 
vibration  to  one  farther  out  from  the  nucleus.  This  is  equivalent  to  in- 
creasing the  atomic  energy,  and  the  increase,  which  came  from  an  out- 
side source,  is  given  out  as  monochromatic  radiation  when  the  electron 
falls  toward  the  nucleus. 


i6 

Of  the  work  on  the  structure  of  the  atom  none  is  more  interesting  than 
that  of  Nicholson,  a  number  of  his  predictions  from  a  theoretical  stand- 
point having  been  confirmed  in  a  most  spectacular  way.  His  work  is 
also  of  extreme  interest  to  chemists,  since  it  deals  with  elements  which 
have  not  as  yet  been  discovered  on  the  earth.  For  a  considerable  time 
it  has  been  known  that  there  are  at  least  two  important  elements  which 
are  recognized  by  their  spectrum,  but  which  have  not  as  yet  been  dis- 
covered on  earth.  A  number  of  spectral  lines  of  unknown  origin  were 
known  to  be  given  by  the  corona  of  the  sun,  and  these  were  attributed  to 
an  element  coronium,  while  the  lines  of  unknown  origin  emitted  by  the 
nebulae  were  supposed  to  be  due  to  an  element  which  was  given  the  name 
nebulium.  The  chief  line  of  its  spectrum  is  the  line  Xsooy .  Nicholson 
was  able,  by  the  assumption  that  certain  lines  belong  to  the  spectrum 
of  nebulium,  to  calculate  the  wave  lengths  of  all  of  the  other  lines  but 
two,  for  which  he  was  altogether  unable  to  account.  Just  at  the  time  when 
Nicholson  made  his  calculation,  Wolf  of  Heidelberg  was  engaged  in  the 
study  of  these  same  lines  in  the  spectra  of  the  nebulae,  and  he  found  that 
certain  lines,  which  had  formerly  been  attributed  to  nebulium,  acted 
differently  from  the  others.  He  found,  for  example,  that  in  the  ring  nebula 
in  Lyra,  discovered  by  Darquier  in  1779,  certain  of  these  lines  were  emitted 
by  the  interior,  and  others  by  its  outer  part.  The  remarkable  part  of 
this  discovery  was  that  the  two  lines  which  were  thus  shown  to  have 
different  origin  from  the  true  lines  of  nebulium,  were  just  the  two  lines 
which  Nicholson  was  unable  to  connect  theoretically  with  the  spectrum 
of  nebulium.  Another  of  Nicholson's  predictions,  which  was  confirmed 
in  a  remarkable  manner,  was  that  of  the  existence  of  a  new  nebulium  line 
of  wave  length  4352.9.  On  photographing  the  spectrum,  Wright,  of 
the  Lick  observatory,  found  this  line,  and  on  looking  over  his  older  photo- 
graphs, he  found  the  line  on  a  plate  taken  several  years  before  the  pre- 
diction of  its  existence  was  made,  but  the  line  was  so  weak  that  it  had  es- 
caped observation. 

In  an  extremely  long  series  of  papers  Nicholson30  has  arrived  at  a  very 
comprehensive  theory  of  spectra,  and  has  applied  it  to  such  problems 
as  cosmic  evolution.  It  gives  a  picture  of  operations  in  vast  nebulae, 
many  light  years  in  extent,  in  connection  with  atomic  and  subatomic 
structure;  changes  occupying  milleniums  of  time  are  discussed  in  connec- 
tion with  those  occurring  in  a  fraction  of  a  second.  Its  very  comprehen- 
siveness causes  some  skepticism,  but  the  remarkable  results  he  has  ob- 
tained would  seem,  in  part  at  least,  to  justify  the  theory. 

Nicholson  also  uses  an  atom  of  the  Rutherford  type,  in  which  the  elec- 
trons are  vibrating  in  orbits  around  the  positive  nucleus.  All  of  Nichol- 
son's work  is,  however,  based  on  calculations  made  by  the  classical  me- 
chanics. The  quantum  hypothesis  is  not  introduced  to  obtain  any 


of  the  results,  but  in  the  course  of  his  work,  Nicholson  shows  how  the 
results  seem  to  be  related  to  this  hypothesis. 

One  of  the  interesting  points  of  this  theory  is  that  the  energy  which 
goes  into  the  spectrum  is  secured  from  the  outside,  and  isjiot,  as  originally 
in  the  theory  of  Bohr,  atomic  energy.  This  would  seem  to  be  much 
more  probable. 

The  electrons  are  considered  as  moving  in  a  steady  state,  in  a  ring 
around  the  nucleus.     Outside  forces  acting  on  these  cause  them  to  take 
up  a  vibration  perpendicular  to  the  plane  of  the  ring.     There  are  several 
modes  of  vibration,  depending  on  the  number  of  electrons  in  the  ring. 
The  strongest  vibration  would  have  a  frequency  equal  to  the  frequency 
of  the  electrons  in  the  ring.     This  is  expressed  by  q  =  co,  or  g/co  ==  i.     In 
vibrations  of  class  zero  the  entire  ring  vibrates  as  a  whole,  always  keeping 
parallel  to  its  original  position.     The  second  class  of  vibration  consists 
in  the  ring  vibrating  in  halves.     That  is,  there  are  two  nodes  and  two 
crests  in  the  wave  which  travels  around  the  ring.     It  is  evident  that  there 
are  as  many  classes  of  vibrations  as  there  are  electrons  in  the  atom.     The 
vibrations  of  the  higher  classes  would  not  be  expected  to  be  strong,  and 
Schott  has  shown  that  the  vibrations  of  a  class  higher  than  three  would 
not  ordinarily  be  strong  enough  to  see.     The  mathematical  analysis  is 
largely  the  same  as  that  developed  by  J.  J.  Thomson  in  his  work  on  his 
atomic  model,  and  will  not  be  given  completely  here.     Only  the  results 
which  are  used  directly  will  be  reproduced. 
e    =  charge  on  an  electron. 
a   =  radius  of  the  ring. 
v    =  no.  charges  in  nucleus. 
m  =  mass  of  an  electron. 
q/u>  =  frequency  of  revolution. 
The  equation  for  the  period  of  vibration  which  Nicholson  obtains  is 

mq2  =  e*/8a*  (Sv  +  P*  +  P0) 

where 

STT/H  csc*  sir/n) 


and 

P0  =  Sw~   l  (i  .  cscz  sir/n). 

There  may  be  as  many  values  of  the  period  as  there  are  of  P*,  which  is 
as  many  as  the  number  of  electrons,     k  is  called  the  class  of  the  vibra- 

tion. 

The  first  atom  which  Nicholson  considered  was  one  in  which  the  num 
ber  of  positive  charges  in  the  nucleus  is  four.     That  is,  v  =  4.     This  atom 
he  has  called  nebulium.     First  consider  the  neutral  atom,  in  which  there 
are  four  negative  electrons.     The  period  equation  may  be  written  as 
masq2  =  e2  [v  +  (Pk  —  P0)/8],  k  =  o,  i,  2,  etc. 


i8 


If  a)  =  the  angular  velocity  of  the  ring,  the  force  of  an  electron  towards 
the  center  is  mato2.  The  radial  attraction  of  the  positive  nucleus  is  ve*/a2. 
The  combined  action  of  the  other  electrons  gives  a  radial  repulsion  of 
<?2SB/4a2  where  Sn  =  Sn—1  esc  sir/n.  Therefore, 

wow2  =  e*/a2  (v  —  8^/4)     or    e*/mas  =  co2  (v  —  S«/4) 
is  the  equation  for  the  steady  state  of  the  neutral  atom.     The  period  equa- 
tions of  this  system  then  become 

16 


<?2/co2  = 


15 


8 


\'2 


k  =  o 


k   = 


or 


=  (1 


146533,    i,    0.849778) 
Correcting  for  a  stationary  observer,  and  introducing  negative  values  of  k, 
q/u   =    (1.146533,1.150222,       2,       2.849778,       4) 

k    =    O         k    =    -  2       k   =    I       &    =    2,       &   =   3 

In  wave  lengths  (C  =  velocity  of  light)  and  considering  a  vibration  in 
the  plane  where  q  =  u,  which  we  would  expect  to  be  strong, 
X  =  271-C/co  (i,  0.872194,  0.86939). 

The  first  value  is  for  q  =  co,  the  second  for  k  =  o,  the  third  for  k  =  —  2. 

The  chief  nebular  line  is  X  =  5006  .9.  If  this  is  chosen  as  the  funda- 
mental line,  then  (5006.  9)  (0.872  194)  =  4367.0  should  be  the  next  line 
of  this  set.  A  strong  line  is  known  at  4363  .  4.  Also  (5006  .  9)  (o  .  86939)  = 
4352.9  should  be  the  next.  At  the  time  of  this  work,  no  line  was  known 
at  4352  .  9  but  it  was  afterward  found  by  Wright31  of  the  Lick  Observatory, 
and  measured  as  4352.3.  Nicholson  made  similar  calculations  for  this 
atom  with  2,  3,  5,  and  6  electrons.  The  results  are  given  below: 

q  - 


&-0. 


—  2. 


27TC/CO    X 


n  = 


n  =  « 


I 

0.81934 

4959.0 

4063  .  2 

4959 

4059.0 

0.80991 

0.81573 

3838.  ga 

3869.0 

3835-8 

3869. 

0.9250 

(o.6666) 


=  5 

4743-0 
4740-0 

i 

4026.80  3724.8 
4026.8  3729.0 

i    0.96826 
3967.60  3841-5 
3967.6  3835-8 

"a"  placed  after  a  wave  length  shows  that  this  one  was  assumed  for  that  particular 
series. 


19 

The  first  method  of  attack  used  by  Nicholson  is  briefly  this,  as  is  seen 
from' the  previous  work.  Making  use  of  the  theoretical  analysis,  he  ob- 
tains the  ratios  of  the  wave  lengths  of  what  might  be  called  a  series,  but 
not  their  absolute  values.  If  a  value  for  one  of  them  is  assumed,  the  rest 
are  given.  The  agreement  in  some  cases  is  far  from  good,  and  later  it 
was  found  necessary  to  consider  certain  of  the  lines  as  due  to  a  different 
source  than  given  here.  It  is  not  clear  as  to  why  in  the  series  for  n  =  5 
for  instance,  the  line  for  k  =  — 2  should  appear,  and  not  the  one  f or  k  =  2, 
or  for  the  vibrations  which  should  be  still  stronger,  k  =  i. 

It  will  be  seen  that  there  is  an  error  of  about  4  A°  in  a  large  number  of 
these  calculated  wave  lengths.  Nicholson  shows  that,  except  in  the  case 
of  the  vibration  of  Class  O,  this  can  be  accounted  for  by  the  fact  that  the 
velocity  of  the  electron  is  not  small  compared  with  that  of  light,  or  at  least 
is  not  small  enough  so  that  it  can  be  neglected  without  error.  He  calcu- 
lates that  the  error  due  to  this  cannot  be  greater  than  about  one  part  in 
a  thousand,  which  amounts  to  about  4  A°  with  the  wave  lengths  consid- 
ered. 

Bromwich  pointed  out  to  Nicholson  that  in  the  case  of  the  vibration 
of  Class  O,  the  mass  of  the  electron  and  the  nucleus  did  not  cancel  out, 
but  that  a  correction  term  of  the  form 

(i  +  nw/M) 

should  be  introduced  into  the  period  equation.     If  H  is  the  value  of  M 
for  a  hydrogen  atom,  then 

w/H  =  o .  00054  approximately. 

This  makes  it  possible  to  calculate  the  atomic  weight  of  nebulium,  which 
gives  the  value  1.3. 

Using  this  method  of  ratios,  Nicholson  has  calculated  the  wave  lengths 
of  lines  for  systems  of  v  =  2,  3,  5,  and  6.  For  v  =  2  and  3,  the  lines  were 
found  by  Wolfe  in  the  nebulae,  v  =  5  was  found  in  the  solar  corona, 
where  Nicholson  accounted  for  21  out  of  27  lines  found. 

For  the  systems  20,  42,  50,  and  6e,  calculations  have  been  made  for  the 
atomic  weight  by  the  method  described  above.  From  the  values  ob- 
tained, it  can  be  shown  that  the  atomic  weights  of  these  simple  ring  sys- 
tems are  proportional  to  the  squares  of  the  number  of  charges  on  their 
nuclei.  For  the  entire  series,  the  results  are  as  follows : 

Element Pr.H  ...  ...  Nu  Pf  Arc 

Atomic  no le ,  2e  30  40  50  6e 

Atomic  wt 0.082         0.327         0.736         1.31         2.1         2.9 

Ratio i2  22  32  42  52  62 

Here  is  a  relation  involving  N2  as  in  Moseley's  work. 
Up  to  this  point,  Nicholson  used  his  method  of  ratios,  and  thus  calcu- 
lated the  wave  lengths  of  the  most  of  the  unknown  lines  in  the  nebulae 


2O 

and  the  solar  corona,  and  succeeded  in  securing  approximate  values  for 
the  atomic  weights.  No  connection  has  as  yet  been  shown  to  exist  be- 
tween the  systems  of  different  nuclear  charge.  This  relation  is  brought 
out  later.  Also,  no  relation  has  been  shown  between  the  principal  fre- 
quency of  vibration  of  the  systems  of  the  same  nuclear  charge,  with  vary- 
ing numbers  of  electrons.  This  relation  is  shown  by  the  consideration 
of  the  energy  of  the  systems  involved. 

As  Nicholson  points  out,  it  is  impossible  to  know  the  absolute  energy 
of  the  atom,1  but  changes  of  energy  may  be  used.  By  a  very  simple  anal- 
ysis Nicholson  arrives  at  the  following  equation  of  energy  of  the  atom, 
in  which  the  term  D  is  equal  to  the  energy  in  a  standard  configuration: 

l/z  mnv2  =  ne2/a  (v  —  l/±  SM)  +  D 
By  the  condition  of  steady  motion, 

wa3co2  =  e2  (v  —  A/4  Sn)  =  mav2. 
Now,  co  =  27rC/X',  where  X'  is  the  principal  wave  length.     This  gives 

„  „    27T       mn  {  e2    ,        \  /  &  \      r*i»/i\V« 
wwa2co2  .  --  =  -  -  (v  —  74 SJ  27rC>  /8X /3. 

co         C   (  m  y 

Therefore  it  is  seen  that  the  ratio  of  energy  to  frequency  is  proportional 
to  n(v  —  Y*  S«)  *X  •  i  and  for  convenience  this  will  be  called  the  atomic 
energy,  E.  Then  E  =  n(v  —  l/t  SW)V'X1/3. 

Now  the  calculation  of  E  for  the  various  atoms  of  protofluorine  where 
v  =  5,  gives  the  following  result: 

n  —  5.  n  =  4.  n  =»  3.  n  •»  2. 

E ,      187.04  164.6  134-7  97-4 

If  7 . 482  is  chosen  as  the  unit  of  energy,  the  number  of  units  for  the  differ- 
ent systems  is  as  follows: 

n  •»  5.        n  =  4.  n  —  3.        n  —  2.         n  -  1.     n  —  0. 

25  22  18  13  70 

Differences 3  4  5  6  7 

Units  per  electron 5  5.5  6  6.5  7  o 

It  is  now  possible  to  calculate  the  wave  length  of  the  line  of  principal 
frequency  for  the  system  >n  =  2.  For  this  system  it  is  seen  that  there  are 
6 . 5  units  of  E  per  electron,  therefore 

E  =  2  (6.5  X  7-482)  =  2  (5  —  1AS2)X1/8  (S2  =  i.ooo). 

From  this  X  =  5073.     A  weak  line  is  known  at  this  point. 

If  the  energy  of  one  of  these  systems  is  decreased  by  radiation  by  cer- 
tain discrete  amounts,  we  would  expect  a  series  of  lines  of  some  sort  to  be 
the  result.  That  is,  a  series  of  spectrum  lines  might  emanate  from  atoms 

1  Equations  have  been  developed  from  the  standpoint  of  both  the  electromagnetic 
theory  and  the  theory  of  relativity,  which  give  the  total  energy  of  an  atom  in  terms  of 
its  mass,  but  it  is  of  course,  not  certain  that  these  equations  are  valid. 


21 

whose  internal  angular  momenta  have  run  down  by  discrete  amounts 
from  'a  standard.  In  the  case  of  protofluorine  with  two  electrons,  the 
loss  of  energy  would  be  expected  to  be  large  enough  so  that  the  series 
could  be  observed.  The  wave  lengths  of  the  lines  of  this  series  may  be 
expressed  by  the  formula 

X  =  (97.107/2  —  i.  223r)3/(4-75)2- 

That  is,  the  energy  E  is  being  decreased  by  an  amount  2  .  2446  each  time. 
The  term  r  takes  successively  the  values  i,  2,  3,  etc.  The  series  is  as 
follows  : 

r  ................  o  i  2  3  4  5  6 

Calculated  ........     5073         4725         440x5         4086.5         3788         3506         3238 

Observed  .........     5073         4725         4400        4087  .4  .  .  3505 

All  these  are  weak  lines.  It  may  be  pointed  out  that  this  method  of 
calculating  a  series  is  very  similar  to  Bohr's  method  where  he  decreases  the 
internal  energy  of  the  atom  by  discrete  amounts  to  give  the  members  of 
the  series.  Bohr  has  given  some  sort  of  an  idea  as  to  how  this  takes  place, 
while  Nicholson  merely  states  that  the  energy  is  lost  by  radiation.  Such 
vibrations  as  give  rise  to  this  type  of  series  are  vibrations  in  the  plane 
of  the  ring,  as  in  Bohr's  model.  It  will  be  noted  later  that  Nicholson 
makes  considerable  use  of  this  method,  even  discarding  his  original  iden- 
tifications of  some  of  the  nebulium  and  protofluorine  lines,  and  putting 
them  into  series  of  this  type. 

If  Q  equals  the  number  of  quanta  of  energy  per  electron,  choosing  as  a 
unit  the  value  h/\^  where  h  is  Planck's  unit,  a  still  more  useful  equation 
is  obtained, 


0.06235 

For  the  atom  of  protofluorine  where  v  =  5,  the  various  values  of  Q  are  as 
follows  : 

«  ..................        5  4  3  2 

Q  .................    600  658.5  718  778.5 

These  values  of  Q  can  easily  be  shown  to  be  in  the  ratio  of  10  :  u  :  12  : 
13  :  14. 

In  the  case  of  Pf  just  dealt  with,  the  value  of  Q  may  be  expressed  by  a 
function  of  the  following  type:  * 

Q  =  A  +  En  +  Cw2 

where  A,  B,  and  C  are  constants.  If  such  a  formula  is  to  be  applied  to 
other  atoms  than  Pf,  these  terms  may  not  be  constants,  but  functions  of 
the  nucleus.  Since  the  function  E/w  has  been  shown  to  be  harmonic, 
it  may  be  supposed  that  the  function  E/V  would  be  of  the  same  general 
type,  that  is: 


22 

where  v  =  n,  a  neutral  atom.     Therefore  the  function  E/w  for  any  atom 
is  of  the  form 

E/w  =  A  +  Ev  +  Cv2  —  n(D  +  EJ>)  +  G«2. 

Since  E  in  all  cases  is  very  closely  a  multiple  of  Planck's  unit,  the  con- 
stants A  to  G  will  be  close  to  whole  numbers.  The  divergencies  might  be 
due  to  the  rotation  of  the  nucleus  of  the  atom  as  a  whole,  at  the  expense 
of  the  angular  momentum  of  the  system,  which  otherwise  might  be  ex- 
actly a  multiple  of  h/2ir.  Nicholson  calculates  the  values  of  these  con- 
stants from  the  case  of  Pf,  and  then  uses  this  method  for  the  recalcula- 
tion of  the  lines  of  the  sytem  4^,  nebulium.  He  finds  that  it  is  necessary 
to  change  the  source  of  a  number  of  the  lines  from  that  given  them  by 
his  first  method.  More  of  them  are  now  thought  of  as  coming  from  vibra- 
tions which  fall  into  the  type  of  series  where  the  cube  roots  of 
the  wave  lengths  differ  by  constant  amounts,  as  in  the  series  calculated 
for  the  system  v  =  5,  n  —  2.  The  value  of  Q  for  such  series  can  be  found 
from  a  formula  of  the  type  used  in  the  series  just  referred  to  : 

Q  =  (Qn/i8r), 
where  r  is  variable,  taking  successively  the  values  i,  2,  3,  etc. 

The  law  relating  the  number  of  quanta  of  positive  and  negative  sys- 
tems is: 


A  series  might  arise  from  negatively  charged  systems,  from  the  energy 
disturbances  due  to  the  repulsion  of  negative  electrons  by  the  system. 
Such  series  might  be  expected  to  be  quite  strong.  A  neutral  system 
would  be  unaffected  by  electrons,  only  becoming  ionized  by  virtue  of  its 
own  unstable  vibrations. 

Some  very  important  relationships  may  be  brought  out  by  the  consid- 
eration of  the  relations  between  the  energy  of  the  various  neutral  systems 
of  different  nuclear  charge.  If  the  principal  wave  length  of  the  system 
is  known,  it  is  possible  to  calculate  the  value  of  E/w  from  the  formula 


The  values  of  E/w  for  the  systems  v  =  5,  4,  and  2  are  600,  576.08,  and 
374.04,  respectively.  These  are  three  terms  of  the  following  harmonic 
sequence  : 

"  ................  5                      4                          3                            2                             i 

E/w  .............  600            576.08             500.76              374-04               195-92 

Difference  ........  23.92                 75-32  126.72                 178.12 

Second  diffe;ence.  .  54  .40                 54.  40                   54.  40 

As  stated  before,  it  might  be  expected  'that  these  values  of  H/v,  which 
are  obviously  the  same  as  E/w,  could  be  expressed  by  the  formula 


23 

The  -following  three  equations  can  be  solved  for  the  constants: 

600.00  =  a  +  5/3  +  257  (i) 

576.08  =  a  +  4)3  +  167  (2) 

500.76  =  a  +  30  +     97  (3) 

and  a  =  — 32,    /3  =  254.4,    7  =  — 25.6.     Therefore 
Q  =  E/V  =  254.4^  —  25.6^  —  32. 

If  the  values  of  E/v  for  the  systems  6e,  je,  8e,  qe  and  loe  are  calculated 
the  following  results  are  obtained: 

v 6  7  8  9  10 

EA 572.52          493.64          363-36          181.68        — 51.40 

The  fact  that  f or  v  =  10  the  energy  is  negative  points  to  the  fact  that 
there  are  only  9  simple  ring  systems  possible.  If  the  first  one  is  left  out 
of  consideration,  and  hydrogen  is  not  put  in  the  periodic  table,  the  num- 
ber of  simple  ring  systems  is  the  same  as  the  number  of  groups  in  the 
first  two  rows  of  the  periodic  table.  It  will  be  shown  later  that  the  sim- 
ple ring  system  le  is  very  closely  related  to  hydrogen  so  that  leaving  them 
both  out  of  consideration  at  this  point  has  some  justification,  particularly 
as  the  place  of  hydrogen  in  the  table  is  very  uncertain. 

Knowing  the  value  of  EA  for  the  various  systems,  it  is  possible  to  find 
their  principal  frequencies  from  the  following  formula: 
=  /E  0.06235 \3  i_ 

„      /    (y_l/4SM)2 

v 6  7  8  9 

X 2613.57       1323-12       431-02        45.15 

All  these  are  outside  of  the  range  of  observation,  but  it  will  be  shown 
later  that  the  first  of  these  exists  in  the  nebulae,  and  it  has  been  given  the 
name  arconium.  It  will  also  be  shown  that  the  system  le  exists,  and  it 
has  been  given  the  name  protohydrogen.  Its  principal  wave  length  is 
calculated  as  1823.55,  which  is  exactly  one-half  the  limit  of  the  B  aimer 
formula  for  hydrogen. 

The  system  2e  is  present  in  the  nebulae,  and  in  Nova  Persei.  The  atom 
with  nucleus  30  is  also  present  in  the  nebulae,  but  its  lines  are  not  as  strong 
as  those  of  ze.  The  system  40  is  nebulium  and  gives  rise  to  the  strongest 
nebular  lines.  Protofluorine,  50,  has  not  been  found  in  the  nebulae,  but 
is  one  of  the  main  constituents  of  the  solar  corona.  As  just  stated,  6e, 
arconium,  and  the  system  70  are  found  in  the  nebulae. 

The  remarkable  agreement  of  these  theories  of  Nicholson's  with  the 
facts  would  seem  to  indicate  that  there  is  here  an  extremely  broad  founda- 
tion for  a  system  on  which  the  building  up  of  the  chemical  elements  may 
rest.  The  relations  between  the  energy  of  these  systems  seems  to  indi- 
cate that  the  principle  of  the  constancy  of  angular  momentum  may  be  the 


24 

physical  basis  of  Planck's  theory  and  also  the  basis  of  all  the  possible 
arrangements  of  electrical  charges  into  the  form  of  ordinary  matter. 

One  of  the  most  important  and  interesting  pieces  of  work  which  Nichol- 
son has  done  is  in  connection  with  the  spectra  of  the  Wolf-Rayet  stars. 
These  stars  are  considered  by  the  astronomers  as  the  earliest  type  known. 
They  are  regarded  as  being  some  sort  of  evolution  product  of  the  nebulae. 
The  only  ordinary  elements  which  are  present  are  hydrogen  and  possibly 
helium,  although  the  last  is  not  well  represented  unless,  as  Bohr  suggests,* 
the  Pickering  series  is  due  to  this  element.  Nicholson  shows  that  a  num- 
ber of  B  aimer  series  exist  in  these  stars,  and  identifies  them  in  a  remark- 
able manner  with  the  constants  of  the  simple  ring  system  called  nebulium. 

If  the  lines  of  these  stars  are  examined  they  are  found  to  contain  a 
number  of  lines  in  the  ratio  of  5/4.  Thus: 

5285/4228  =  1.2500  5693/4555  =  1-2499 

5813/4652  =  1.2495  5593/4473  =  1.2503 

If  the  Balmer  formula  is  considered  for  one  special  case  the  following  re- 
lationship is  found  : 

X  =  X0w2/w2  —  i 

For  m  —  2  and  4  the  following  results: 

^2  =  4/3  Xo         X4  =  16/15  X0         X2/X4  =  5/4 

This  suggests  that  Balmer  series  exist  in  the  Wolf-Rayet  stars,  and  a  sim- 
ple calculation  gives  the  following: 

X  =  (4104,  3963-5)  w2/™2  —  i 
A  further  examination  of  the  lines  leads  to  the  following  four  series  : 


N 
X  =  (4104,  or  3963-5)   ^^  or  m, 

It  was  found  in  the  previous  work  that  the  three  main  vibrations  of 
the  neutral  nebulium  atom  had  frequencies  in  the  following  ratio: 
?2/a>2  =  i,  1.3145.  0.8496 

Now  0.3286  =  i  .3145/4.  This  shows  that  these  series  are  in  some  way 
related  to  the  nebulium  atom.  It  seems  probable  that  another  series  or 
rather  two  series  might  exist  in  which  the  term  0.3286  was  replaced  by 
one-fourth  of  the  other  ratio  for  the  third  line  of  the  neutral  atom. 

0.8496/4  =  0.2124. 
The  formula  would  then  be. 

X  =  (4104,  3963-5)  w2/w2  —  0.2124. 

Lines  calculated  f  or  m  =  2,  and  3  give  lines  which  are  known  in  these 
stars,  thus  confirming  the  theory. 

*  This  suggestion  is  confirmed  by  the  work  of  Evans. 


25 

In  general  then,  the  formula  for  the  Balmer  series  in  the  Wolf-Rayet 

stars  may  be  written  as 

.  /        m' 
X  =  (4104,  3963-5)  int2_. 


A  search  for  another  limiting  frequency  gives  the  value  5254.     We 
now  have  nine  Balmer  series  which  may  be  written  as 


* 


. 
X  =  (4254,  4J04,  3953-5)^^^7^  cr 

A  consideration  of  the  limiting  wave  lengths  gives  stiU  another  way 
of  expressing  these  formulae.  If  they  are  written  in  wave  numbers 
their  differences  are  seen  to  be  constant. 

io8/X0  =  25227,  24366.5,  23506 

with  the  constant  difference  860.5.  Therefore  Xo'1  =  A  +  Bn  where 
n  takes  integral  values.  Substituting  values  for  this  and  rearranging  it, 
the  following  formula  for  the  Balmar  series  in  the  Wolf-Rayet  stars  is 
obtained  : 

\  2Xo        .  or 

= 


. 

i  +nd          —  42/4"2         m2 

in  which  X0  =  5007,  the  principal  wave  length  of  the  neutral  atom  of 
nebulium,  n  takes  successive  integral  values,  and  d  =  0.08609  and  is 
not  arbitrary,  but  is  calculated  from  data  involved  in  the  consideration 
of  the  neutral  nebulium  atom. 

The  above  equation  is  one  of  the  most  remarkable  and  important 
points  of  Nicholson's  work,  for  in  it  he  succeeds  in  bringing  together  the 
simple  ring  systems  which  are  not  known  on  the  earth,  and  our  ordinary 

elements. 

It  is  evident  that  a  change  in  the  term  n  means  a  change  of  some 
in  the  atom.  It  is  also  evident  that  it  must  be  of  a  character  that  the 
force  between  the  component  parts  does  not  change.  It  seems  inevitable 
that  the  change  must  consist  in  a  change  in  the  nucleus,  which  does  not 
alter  its  charge.  It  is  significant  that  the  simple  ring  systems  seem  to 
be  incapable  of  giving  rise  to  Balmer  series,  and  the  only  logical  conclu- 
sions is  that  they  depend  on  the  intimate  structure  of  the  nucleus.  The 
elements  which  give  rise  to  Balmer  series  may  then  be  looked  upon  as  the 
evolution  products  of  the  simple  ring  system  on  which  the  value  of  X0 
depends.  This  is  considering  X0  as  belonging  to  any  simple  ring  syst 
and  not  to  nebulium  alone. 

Nicholson  shows  that  the  simple  ring  system  le  can  have  only  one 
vibration  frequency,  q  =  co.     This  has  already  been  calculated  as  X  = 
1823.35,  which  is  exactly  one-half  of  the  limiting  wave  length  of 
mer  series  for  hydrogen.     From  the  formula 


26 

2X0      /     m 
i  +  nd  \w> 

it  is  seen  that,  to  derive  the  hydrogen  Balmer  formula,  n  must  be  equal 
to  o.  That  is,  hydrogen  would  appear  to  be  the  first  evolution  product 
of  the  system  le,  protohydrogen. 

It  should  be  noted  that  Nicholson  has  in  a  rather  round-about  way 
succeeded  in  evaluating  the  Rydberg  constant  even  more  closely  than 
did  Bohr.  He  has  not,  however,  attempted  to  give  any  physical  pic- 
ture of  the  mechanism  of  the  production  of  the  Balmer  series. 

While  up  to  the  present  time  the  evolution  products  of  the  other  sys- 
tems are  not  known  in  general,  it  is  likely  that  they  may  be  some  of  our 
terrestrial  elements.  The  lines  due  to  a  number  of  the  evolution  products 
of  nebulium  are  shown  in  the  Wolf-Rayet  stars. 

No  work  has  yet  been  published  connecting  helium  with  the  simple 
ring  systems,  although  from  the  fact  that  it  appears  in  the  nebulae  and 
the  stars  about  the  same  time  as  does  hydrogen,  it  seemed  likely  that  it 
is  one  of  the  early  evolution  products  of  one  of  the  systems.  In  some  work 
as  yet  unpublished  Nicholson  has  succeeded  in  showing  that  helium  is 
the  evolution  product  of  the  system  20. 

From  the  progressive  changes  of  the  spectra  of  the  stars,  and  other  evi- 
dence which  points  to  their  age,  it  seems  likely  that  all  of  our  common 
elements  are  more  complex  forms  of  matter  than  the  simple  ring  systems 
and  hydrogen,  and  are  built  up  from  them.  In  such  spectra  the  elements 
make  their  appearance  in  the  order  of  their  atomic  weights. 

According  to  Nicholson's  idea,  then,  our  ordinary  terrestrial  elements 
are  evolution  products  of  the  simple  ring  systems  found  in  the  nebulae 
and  the  stars.  That  is,  they  have  nuclei  which  are  complex,  containing 
both  positive  and  negative  electrons.  This  is  in  good  accord  with 
other  facts  but  it  does  not  agree  with  Rutherford's  idea  that  the  nucleus 
of  the  hydrogen  atom  may  be  the  positive  electron.  If  the  astronomical 
evidence  is  admitted,  it  may  be  safely  assumed  that  in  the  novae  and 
nebulae,  where  the  temperature  is  supposed  by  Nicholson  to  be  very  high, 
the  complex  atoms  are  unstable,  breaking  up  into  simple  ones,  or  if  the 
process  is  looked  at  from  the  other  point  of  view,  as  these  hot  bodies  cool 
the  simple  ring  systems  condense,  becoming  more  complex  and  giving 
rise  to  the  elements  known  on  the  earth. 

The  only  very  important  papers  on  atomic  structure  which  have  not 
been  considered  are  those  of  Stark.  His  work  has  been  omitted  on  ac- 
count of  kck  of  space,  and  because  he  has  not  as  yet  been  able  to  obtain 
from  his  results  any  very  definite  picture  of  the  structure  of  the  atom. 
Another  reason  is  that  this  work  is  already  available  in  book  form31  which 
is  not  true  of  the  material  presented  in  this  paper.  Stark's  greatest  dis- 
coverv  is  that  of  the  electrical  Zeeman  effect,  or  the  Stark  effect,  which 


is  the  decomposition  of  the  spectral  lines  by  means  of  a  static  electrical 
charge  Up  to  the  present  time  this  effect,  which  has  been  made  to  give 
a  much  greater  separation  of  the  components  of  the  lines  than  has  been 
obtained  by  the  Zeeman  effect,  has  been  obtained  only  in  the  spectra 
from  canal  or  positive  rays.  However  this  is  probablr<fcie  to  the  fact 
that  this  is  the  only  method  which  has  been  found  for  securing  the  high 
field  strengths  which  are  essential.  In  Stark's  work  he  has  used  a  poten- 
tial fall  of  from  ten  to  seventy-four  thousand  volts  per  centimeter. 

BIBLIOGRAPHY. 

i.  Kelvin,  Phil.  Mag.,  3,  257  (1902). 
*/2.  Rutherford,  Ibid.,  21,  669  (1911)- 

3.  Geiger  and  Marsden,  Proc.  Roy.  Soc.,  82  A,  495  (1909)- 

4.  Geiger,  Ibid.,  83,  492  (1910). 

5.  Geiger,  Proc.  Man.  Lit.  and  Phil.  Soc.,  55,  pt-  II,  20  (1913);  Phil.  Mag.,  5,  604 

(1913)- 

6.  Nagaoka,  Phil.  Mag.,  7,  445  (1904). 

7.  Rutherford  and  Nuttal,  Ibid.,  26,  702  (1913)- 

8.  Marsden,  Ibid.,  27,  824  (1914)- 

9.  Rutherford,  Ibid.,  27,  448  (1914)- 

10.  Barkla,  Ibid.,  21,  648  (1911)- 

11.  van  den  Broek,  Physik.  Z.,  14,  33  (1913)- 

12.  Bohr,  Phil.  Mag.,  26,  i  (1913)- 

13.  Moseley,  Ibid.,  26,  1024  (1913);  27,  703  (1914)- 

14.  Laue,  Ann.  Physik,  41,  989  (1913).. 

15.  Bragg  and  Bragg,  Proc.  Roy.  Soc.,  88A,  428  (1913);  Ibid.,  SgA,  246  (1914;- 

16.  Barkla  and  Sadler,  Phil.  Mag.,  16,  550  (1908). 

17.  Aston,  Eng..  96,  423  (1913)- 

1 8    Russell  and  Ross,  Proc.  Roy.  Soc.,  87A,  478  (1912). 

19.  Exner  and  Haschek,  Sitzb.  K.  Akad'.  Wiss.  Wien.,  121,  175  (1912). 

20.  Soddy,  Chem.  News,  107,  97  (1913)- 

21.  Fajans,  Ber.,  46,  422  (1913)- 

22.  Rutherford  and  Andrade,  Phil.  Mag.,  27,  867  (1914)- 
23    Richards,  Jour.  Am.  Chem.  Soc.,  36,  1329  (1914)- 

24.  Soddy,  /.  Chem.  Soc.,  105,  1402  (1914);  Curie,  Compt.  rend.,  158,  1676  (1914). 

25.  Soddy,  Nature,  94,  615  (1915)- 

26.  Bohr,  Phil.  Mag.,  26,  476,  857  (1913)- 

27.  Evans,  Ibid.,  29,  284  (1915)- 

28.  Bohr,  Ibid.,  29,  332  (1915)- 

29.  Nicholson,  Ibid.,  27,  541  (1914);  28,  9O  (1914)- 

30    Nicholson,  Mon.  Not.  Roy.  Ast.  Soc.,  72,  49  (i9«);  72,  139  (i9M)S  72,  677 
(1912);  72,  729  (1912);  73,  382  (1912);  74,  "8  d9i3);  74,  204  (1913);  74,  425  (I9I3)? 
74,  486  (I|^ 74^623^^4).^  Quaiiten/,  s  Hirzd>  Ldpzig  (I9IO).  «Die  elementare 
Strahlung,"  S.  Hirzel,  Leipzig  (1911);  "Elektrische  Spektralanalyse  chemischer  Atome," 
S.  Hirzel,  Leipzig  (1914).     Contains  a  bibliography.     J.  J.  Thomson, 
between  Atoms  and  Chemical  Affinity,"  Phil.  Mag.,  27,  757  (1914);  Rutherford  and 
Robinson,  Ibid.,  26,  342,    937    (1913);  Darwin,  "The  Theory  of  X-ray  Reflection,^ 
Ibid    27,  315    675  (1914) ;  Hicks,  "Effect  of  the  Magneton  in  the  Scattering  of  X-rays 
Proc    Roy.  Soc.,  9oA,  356  (1915);  van    den    Broek,  "On  Nuclear  Electrons,"  Phil. 


28 

Mag.,  27,  455  (1914);  J.  H.  Jeans,  "Report  on  Radiation  and  the  Quantum  Theory 
to  the  Physical  Society  of  London"  (1914);  Fowler,  "The  Pickering  Series  Spectrum," 
Bakerian  Lecture,  1914;  Phil.  Trans.  A.,  214;  Proc.  Roy.  Soc.t  poA,  426  (1915);  Cre- 
hore,  "Theory  of  Atomic  Structure,"  Phil.  Mag.,  29,  310  (1915). 

X-ray  spectra:  Bragg,  W.  H.,  Nature,  91,  477  (1912);  Bragg,  W.  H.  and  W.  L., 
Proc.  Roy.  Soc.,  88A,  426  (1913);  Bragg,  W.  L.,  Phil.  Mag.,  28,  355  (1914);  Bragg, 
W.  H.,  Eng.,  97,  814  (1914);  Bragg,  W.  L.,  Proc.  Roy.  Soc.,  8pA,  241  (1914);  Ibid., 
8pA,  248  (1914):  Bragg,  W.  H.  and  W.  L.,  Ibid.,  89A,  277  (1914);  Bragg,  W.  H.,  Ibid., 
SgA,  430  (1914);  Bragg,  W.  L.,  Ibid.,  SpA,  468  (1914);  Bragg,  W.  H.,  Ibid.,  8pA,  575 
(1914)- 


Part  II 

The  Changes  of  Mass  and  Weight  Involved  in  the 
Formation  of  Complex  Atoms 


In  the  study  of  the  important  question  of  the  structure  and  composition 
of  the  elements,  it  might  seem  that  a  consideration  of  the  relations  exist- 
ing between  the  atomic  weights  should  give  results  of  the  greatest  value. 
Unfortunately,  however,  the  first  suggestions  presented  to  explain  the 
relations  which  probably  exist  were  given  in  such  a  form,  and  were  based 
upon  such  extremely  inaccurate  values  for  the  atomic  weights  that  a  very 
considerable  prejudice  has  been  developed  against  similar  hypotheses. 

The  first  important  hypothesis  in  regard  to  atomic  weight  relations 
appeared  in  two  anonymous  papers  in  the  Annals  of  Philosophy  for 
1815  and  1816,  just  one  hundred  years  ago.  These  papers  were  known 
to  have  been  written  by  Prout,  whose  ideas  as  they  were  presented  re- 
ceived the  vigorous  support  of  Thomson,  considered  in  England  as  the 
leading  chemical  authority  of  his  day;  and  many  years  later,  from  1840 
to  1860,  they  were  very  strongly  advocated  by  Dumas,  who  made  a 
large  number  of  atomic  weight  determinations  during  this  period.  Very 
many  other  chemists,  among  them  Gmelin,  Erdmann,  and  Marchand, 
were  also  numbered  among  Prout's  supporters.  On  the  other  hand,  Stas, 
who  in  the  beginning  tried  to  aid  Dumas  in  the  revival  of  Prout's  hypoth- 
esis, afterward  designated  it  as  a  pure  fiction,  and  Berzelius  at  all  times 
adhered  to  the  view  that  the  exact  atomic  weights  could  not  be  deter- 
mined except  by  experiment. 

The  prejudice  which  existed  a  few  years  ago  against  Prout's  idea  is 
well  shown  by  a  quotation  from  von  Meyer's  History  of  Chemistry, 
printed  in  1906. 

"During  the  period  in  which  Davy  and  Gay-Lussac  were  carrying  on  their  brilliant 
work,  and  before  the  star  of  Berzelius  had  attained  to  its  full  luster,  a  literary  chemical 
event  occurred  which  made  a  profound  impression  upon  nearly  all  the  chemists 
of  that  day,  viz.,  the  advancement  of  Prout's  hypothesis.  This  was  one  of  the 
factors  which  materially  depreciated  the  atomic  doctrine  in  the  eyes  of  many 
eminent  investigators.  On  account  of  its  influence  upon  the  further  development 
of  the  atomic  theory  this  hypothesis  must  be  discussed  here,  although  it  but  seldom 
happens  that  an  idea  from  which  important  theoretical  conceptions  sprang,  originated 
in  so  faulty  a  manner  as  it  did." 

Prout's  work  was  not,  as  the  above  quotation  infers,  entirely  "literary," 
for  he  made  a  large  number  of  experimental  determinations  for  use  in  his 
calculations  of  the  specific  gravity  of  the  various  elements,  which  he  as- 


30 

sumed  to  exist  in  the  gaseous  form.  His  experiments  were,  according  to 
his  own  statements,  somewhat  crude,  but  he  also  made  use  of  the  more 
accurate  data  obtained  by  Gay-Lussac,  and  his  work  was  based  upon  the 
volume  relations  of  gases  as  discovered  by  the  French  investigator. 

Exactly  the  form  in  which  the  numerical  part  of  Prout's  hypothesis 
should  be  expressed  in  terms  of  modern  atomic  weights,  it  is  difficult  to 
say,  but  the  principal  point  is  that  his  atomic  weights,  which,  however, 
are  not  comparable  with  those  now  used,  were  expressed  in  whole  num- 
bers, as  given  below  in  two  columns  taken  from  his  table: 
TABLE  I.— PROUT'S  TABLE  OF  THE  MORE  ACCURATELY  DETERMINED  ATOMIC  WEIGHTS. 

Atomic  weight,  2  vols. 
Element.  Sp.  gr.  of  hydrogen  being  1. 

H i  i 

C 6  6 

N 14  14 

P H  14 

0 16  8 

S 16  16 

Ca 20  20 

Na 24  24 

Fe 28  28 

Zn.; 32  32 

Cl 36  36 

K 40  40 

Ba 70  70 

I 124  124 

The  atomic  weights  thus  given  by  Prout  are  within  a  few  units  of  the 
modern  values  in  the  case  of  the  univalent  atoms  and  for  nitrogen;  but 
the  values  given  for  the  atoms  of  higher  valence,  with  the  exception  of 
nitrogen,  are  approximately  half  -the  present  values.  This  would  mean 
that  according  to  Prout's  system,  since  the  atomic  weights  he  gives  are 
whole  numbers,  the  atomic  weights  of  the  present  system  should  be  divisi- 
ble by  two  for  the  atoms  of  higher  valence,  which  is  equivalent  to  the  use 
of  the  hydrogen  molecule  instead  of  the  atom  as  a  unit.  In  this  connec- 
tion it  may  be  noticed  that  his  atomic  weights  are  taken  on  the  basis  of 
"2  volumes  of  hydrogen  being  i." 

Thus,  from  a  numerical  standpoint,  Prout's  hypothesis  does  not  seem 
to  mean  what  is  usually  supposed.  Expressed  in  terms  of  the  composi- 
tion of  what  he  considered  to  be  complex  atoms,  it  is  given  below  in  his 
own  words: 

"If  the  views  we  have  endeavored  to  advance  be  correct,  we  may  also  consider  the 
icpt!)Ti]  i/Xi;  of  the  ancients  to  be  realized  in  hydrogen,  an  opinion  by  the  way,  not 
altogether  hew.  If  we  actually  consider  this  to  be  the  case,  and  further  consider  the 
specific  gravities  of  bodies  in  their  gaseous  state  to  represent  the  number  of  volumes  con- 
densed into  one;  or,  in  other  words,  the  number  of  the  absolute  weight  of  a  single  volume 
of  the  first  matter  which  they  contain,  which  is  extremely  probable,  multiples  in  weight 
must  also  indicate  multiples  in  volume,  and  vice  versa;  and  the  specific  gravities,  or  abso- 


lute  weights  of  all  bodies  in  the  gaseous  state,  must  be  multiples  of  the  specific  gravity 
or  absolute  weight  of  the  first  matter,  because  all  bodies  in  a  gaseous  state  which  unite 
with  one  another,  unite  with  reference  to  their  volume." 

While  it  is  true  that  Prout  had  at  the  time  when  he  presented  it,  no 
real  foundation  for  his  ideas,  more  accurate  work,  while  itrpt=aved  his  sys- 
tem to  be  invalid  from  a  purely  numerical  standpoint,  at  the  same  time 
established  the  fact  that  the  atomic  weights  of  the  lighter  elements,  on 
the  hydrogen  basis,  are  much  closer  to  whole  numbers  than  would  be 
likely  to  result  from  any  entirely  accidental  method  of  distribution. 
Thus  the  deviations  of  the  lighter  elements  are  small,  as  will  be  seen 
by  the  following  table: 

At.  wt.  Deviation  from  a 

Element.  H  =   1.  whole  number. 

He 3-97  0.03 

Li 6 . 89  o .  1 1 

Be 9.03  0.03 

B 10.91  0.09 

C 11.91  0.09 

N 13-90  o.io 

0 15.88  0.12 

F 18.85  o-i5 

The  average  of  these  deviations  is  0.09  unit,  while  the  theoretical 
deviation  on  the  basis  that  the  values  for  the  atomic  weights  are  entirely 
accidental,  is  0.25  unit.  If  the  first  seventeen  elements  are  used  in  the 
calculation,  the  average  deviation  is  found  to  be  o.  15  unit,  while  the  re- 
sult obtained  for  twenty-five  elements  is  0.21.  The  more  complete 
table,  designated  as  Table  II,  gives  these  deviations,  which  are  seen  to  be 
negative  in  almost  every  case,  the  exceptions  being  magnesium,  silicon, 
and  chlorine.  The  exclusion  of  beryllium  from  consideration  in  this  con- 
nection is  due  to  the  fact  that  its  atomic  weight  is  not  known  with  suffi- 
cient accuracy,  and  neon  is  not  taken  into  account,  since  its  positive  varia- 
tion may  be  explained  by  the  discovery  by  Thomson  and  by  Aston  that 
neon  is  a  mixture  of  two  isotopes  of  atomic  weights  twenty  and  twenty- 
two. 

Not  only  is  the  variation  from  a  whole  number  a  negative  number, 
but  in  addition  its  numerical  value  is  nearly  constant,  the  average  value 
for  the  21  elements  being  0.77%,  while  the  six  elements  from  boron  to 
sodium  show  values  of  0.77,  0.77.  0.70,  0.77,  0.77,  and  0.77%.  The 
deviation  is  therefore  not  a  periodic,  but  a  constant  one.  If,  then,  a  modi- 
fication of  Prout's  hypothesis  that  the  elements  are  built  up  of  hydrogen 
atoms  as  units  is  to  be  taken  as  a  working  basis,  it  becomes  important 
to  find  a  cause  for  the  decrease  in  weight  which  would  result  from  the 
formation  of  a  complex  atom  from  a  number  of  hydrogen  atoms.  The 
regularity  in  the  effect  suggests  that,  in  general,  this  decrease  in  weight 
is  probably  due  to  some  common  cause,  though  the  exceptional  cases  of 


H1 
He2 


At.  wt. 
H-  1. 

I  .OOO 

3-97 

6.89 

9-03 

10.91 


Per  cent.  Prob. 

varia-  error 

tion  from  in  at. 

whole  no.  wts. 

0.78      0.0002 
O.OO      O.OI 

0.86      O.OI 

(+I.II)    0.05 


TABLE  II. — DEVIATIONS  OP  THE  ATOMIC  WEIGHTS  FROM  WHOLE  NUMBERS 

2 

Be 
B. 

C! 11.91 

N 13-90 

0 15-88 

F 18.85 

Ne» 19.85 

Na4 22.82 

Mg 24.13 

Al 26.89 

Si 28.08 

P6 30.78 

S8 31-82 

Cl 35-19 

AT 39-57 

K 38.80 

Ca 39-76 

Sc 43-76 

Ti 47.73 

V 50.61 

Cr 51.60 

Mn 54-50 

Fe 55-41 

Co 58.51 

Per  cent,  variation  of  2 1  elements  (omitting  Be,  Mg,  Si,  Cl),  or  the  packing  effect  =  0.77% 
Average  devation  of  the  atomic  weights,  H  =  i,  from  whole  numbers  =0.21 

Theoretical  deviation  of  atomic  weights  from  whole  numbers  on  the  basis  that 

the  deviations  are  entirely  accidental  =0.25 

Average  deviation  of  the  atomic  weights,  H  =  i,  for  the  eight  elements  from 

helium  to  sodium  =  o .  1 1 

Average  deviation  of  the  atomic  weights,  O  =  16,  when  Mg,  Si,  and  Cl  are 

omitted  =0.05 

Average  deviation  of  the  atomic  weights,  O  =  16,  for  the  eight  elements  from 

helium  to  sodium  =0.02 

1  W.  A.  Noyes  ("A  Text -book  of  Chemistry,"  p.  72)  states  that  the  atomic  weight 
used  for  hydrogen,  i  .0078,  is  probably  not  in  error  by  so  much  as  i  part  in  5000. 

2  Heuse  (Verh.  deut.  physik.  Ges.,  15,  518  (1913))  obtained   the  value   4.002  as 
the  result  of  7  experiments. 

3  Leduc  (Compt.  rend.,  158,  864  (1914))  gives  the  atomic  weight  of  neon  as  20.15 
when  hydrogen  is  taken  as  i  .0075.     Leduc's  value  is  not  used,  on  account  of  the  dis- 
covery of  the  complexity  of  neon  as  described  in  the  text  of  the  paper, 

4  Richards  and  Hoover  (Jour.  Amer.  Chem.  Soc.,  37,  95  (1915))  determined  the 
atomic  weights  of  carbon  as  12.005,  and  of  sodium  as  22.995,  and  in  Vol.  37,  p.  108, 
they  give  the  atomic  weight  of  sulfur  as  32 .06. 

6  The  atomic  weight  for  phosphorus  is  taken  as  3 1 . 02  from  recent  determinations 
made  by  Baxter  (Jour.  Amer.  Chem.  Soc.,  33,  1657  (1912)). 


Diff.        Per  cent.    Possible 
from        variation  per  cent 
whole  or  the  pack-  varia- 
number.  ing  effect,     tion. 

Diff. 
from 
At.  wt.           whole 
O  «=  16.        numbei 

1.0078     -fo.oo' 
4.00            o.oo 

—  0 

•03 

-o 

•77     12.5 

—  o 

.11 

—  i 

.62       7.1 

6 

•94 

—  o 

.06 

[+o 

.03) 

5-5 

9 

.1 

+o 

.1 

—  o 

.09 

—  o 

•77       4-5 

II 

.0 

0 

.00 

0 

.09 

—  0 

•77       4-2 

12 

.00 

o 

.00 

—  o 

.10 

—  0 

.70       3.6 

14 

.01 

+o 

.01 

—  o 

.12 

—  o 

•77       3-i 

16 

.00 

0 

.00 

—  o 

•  15 

0 

.77       2.6 

19.00 

o 

.0 

20 

.0 

—  o 

.18 

—  o 

.77          2.2 

23 

.00 

0 

.00 

+o 

•  13 

+o 

•55       2.15 

24 

•32 

+0 

.32 

—  o 

.  II 

—  o 

.40 

•  85 

27 

.1 

+o 

.10 

+o 

.08 

+o 

.31 

.78 

28 

•  3 

+o 

.30 

0 

.22 

0 

•71 

.61 

21 

.02 

+o 

.02 

—  o 

.18 

—  o 

•56 

•56 

32 

.07 

+o 

.07 

+o 

•  19 

+o 

•54 

•43 

35 

.46 

+o 

.46 

—  o 

•43 

—  I 

.07 

•25 

39 

.88 

—  o 

.  12 

—  o 

.20 

—  o 

•52 

.28 

39 

.10 

+o 

.10 

0 

.24 

0 

.60 

•  25 

40 

•  07 

+o 

•07 

—  o 

•  24 

—  o 

•55 

•14 

44 

.  i 

+o 

.10 

0 

.27 

—  o 

•57 

.04 

48 

.1 

+o 

.10 

—  0 

•  39 

0 

•77       0.98 

51 

.0 

o 

.0 

—  o 

.40 

0 

.77       0.96 

52 

.0 

0 

.0 

0 

•  50 

0 

.90       o  .  90 

54 

•  93 

—  0 

.07 

0 

•  59 

—  I 

.06       o  .  89 

55 

.84 

—  o 

.16 

0 

•49 

—  o 

.83       o  .  85 

58 

•97 

0 

•03 

O.OO 
0.00 

+0.07 

O.OO 
0.0 

0.05 
0.005 
0.005 
O.OO 

0.05 

0.00 

O.OI 

+  1-33 

0.03 

+0.37 

O.I 

+  i  .07 

O.  I 

+0.06 

O.OI 

+O.22 

O.OI 

+  I-3I 

O.OI 

0.30 

0.02 

+0.25 

O.OI 

+0.17 

0.03 

+0.23 

0.2 

+0.21 

O.I 

0.0 

O.  I 

0.0 

0.05 

—0.13 

0.05 

O.29 

0.03 

—  0.05 

0.02 

33 

magnesium,  silicon,  and  chlorine,  show  that  there  is  certainly  some  other 
complicating  factor.  The  discovery  of  the  reason  for  the  deviation 
of  the  same  kind  in  the  case  of  neon,  where  it  is  due  to  its  admixture 
with  an  isotope  of  higher  atomic  weight,  suggests  that  it  may  not  be  im- 
possible to  find  explanations  for  these  three  other  exceptions.  In  order 
to  have  a  term  for  the  percentage  decrease  in  weight,  it  may  be  well  to 
call  this  the  packing  effect,  or  the  percentage  variation  from  the  com- 
monly assumed  law  of  summation,  that  the  mass  of  the  atom  is  equal 
to  the  sum  of  the  masses  of  its  parts. 

It  has  formerly  seemed  difficult  to  explain  why  the  atomic  weights 
referred  to  that  of  oxygen  as  16  are  so  much  closer  to  whole  numbers 
than  those  referred  to  that  of  hydrogen  as  one,  but,  the  explanation  is  a 
very  simple  one  when  the  facts  of  the  case  are  considered.  The  closeness 
of  the  atomic  weights  on  the  oxygen  basis  to  whole  numbers,  is  indeed 
extremely  remarkable.  Thus  for  the  eight  elements  from  helium  to 
sodium  the  average  deviation  is  only  0.02  unit,  which  is  less  than  the 
average  probable  error  in  the  atomic  weight  determinations.  When 
twenty-one  elements  are  taken  from  the  table,  omitting  the  exceptional 
cases  of  magnesium,  silicon,  and  chlorine,  the  deviation  averages  only 
0.05  unit,  while  if  these  are  included,  this  is  increased  only  to  0.09 
unit.  These  results  have  been  calculated  without  taking  the  sign  into 
account.  If  the  sign  is  considered  the  average  deviation  is  reduced  to 
o.oi  unit  for  the  twenty-one  elements.  The  probability  that  such  values 
could  be  obtained  by  accident,  is  so  slight  as  to  be  unworthy  of  considera- 
tion. If  an  oxygen  atom  is  a  structure  built  up  from  16  hydrogen  atoms, 
then  the  weight  according  to  the  law  of  summation  should  be  16  times 
i  .0078  or  1 6. 125.  The  difference  between  16. 125  and  1 6.00  is  the  value 
of  the  packing  effect,  and  if  this  effect  were  the  same  for  all  of  the  elements, 
except  hydrogen,  then  the  choice  of  a  whole  number  at  the  atomic  weight 
of  any  one  of  them,  would,  of  necessity,  cause  all  of  the  other  atomic  weights 
to  be  whole  numbers.  Though  this  is  not  quite  true,  it  is  seen  that  the 
packing  effect  for  oxygen  is  0.77%,  which  is  the  average  of  the  packing 
effects  for  the  other  21  elements  considered.  Therefore,  those  elements 
which  have  packing  effects  equal  to  that  of  oxygen  will  have  whole  num- 
bers for  their  atomic  weights,  and  since  the  other  elements  show  nearly 
the  same  percentage  effect,  their  atomic  weights  must  also  lie  close  to 
whole  numbers. 

According  to  this  view,  Prout's  hypothesis  from  the  purely  numerical 
standpoint,  is  entirely  invalid,  but  there  still  remains  the  problem  of 
finding  an  explanation  for  three  facts:  First,  that  the  atomic  weights  of 
the  lighter  elements  on  the  hydrogen  basis  approximate  whole  numbers; 
second,  that  the  deviations  from  whole  numbers  are  negative;  and  third, 
that  the  deviations  are  practically  constant  in  magnitude.  Before  con- 


34 

sidering  any  explanation  of  these  facts  it  is  of  interest  to  consider  the 
following  extremely  interesting  comments  upon  this  subject,  as  written 
by  Marignac  in  1860: 

"We  are  then  able  to  say  of  Prout's  hypothesis  that  which  we  can  say  of  the  laws 
of  Mariotte  and  Gay-Lussac  relative  to  the  variations  of  the  volumes  of  gases.  These 
laws  long  considered  as  absolute,  have  been  found  to  be  inexact  when  subjected  to  ex- 
periments of  so  precise  a  nature  as  those  of  M.  Regnault,  M.  Magnus,  etc.  Neverthe- 
less they  will  be  always  considered  as  expressing  natural  laws,  either  from  the  practical 
point  of  view,  for  they  allow  the  change  of  volume  of  gases  to  be  calculated  in  the  ma- 
jority of  cases,  with  a  sufficiently  close  approximation,  or  even  from  the  theoretical 
point  of  view,  for  they  most  probably  give  the  normal  law  of  changes  of  volume,  when 
allowance  has  been  made  for  some  perturbing  influences  which  may  be  discovered 
later,  and  for  which  it  may  also  be  possible  to  calculate  the  effects.  We  may  believe 
that  the  same  is  true  with  respect  to  Prout's  law;  if  it  is  not  strictly  confirmed  by  experi- 
ment, it  appears  nevertheless  to  express  the  relation  between  simple  bodies  with  suffi- 
cient accuracy  for  the  practical  calculations  of  the  chemist,  and  perhaps  also  the  nor- 
mal relationship  which  ought  to  exist  among  these  weights,  when  allowance  is  made 
for  some  perturbing  causes,  the  research  for  which  should  exercise  the  capacity  and 
imagination  of  chemists.  Should  we  not,  for  example,  quite  in  keeping  with  the  funda- 
mental principle  of  this  law,  that  is  to  say,  in  admitting  the  hypothesis  of  the  unity  of 
matter,  be  able  to  make  the  following  supposition,  to  which  I  attach  no  further  im- 
portance than  that  of  showing  that  we  may  be  able  to  explain  the  discordance  which 
exists  between  the  .experimental  results  and  the  direct  consequences  of  this  principle? 
May  we  not  be  able  to  suppose  that  the  unknown  cause  (probably  differing  from  the 
physical  and  chemical  agents  known  to  us),  which  has  determined  certain  groupings 
of  primordial  matter  so  as  to  give  birth  to  our  simple  chemical  atoms,  and  to  impress 
upon  each  of  these  groups  a  special  character  and  peculiar  properties,  has  been  able  at 
the  same  time  to  exercise  an  influence  upon  the  manner  in  which  these  groups  of  atoms 
obey  the  law  of  universal  attraction,  so  that  the  weight  of  each  of  them  is  not  exactly 
the  sum  of  the  weights  of  the  primordial  atoms  which  constitute  it?" 

It  has  usually  been  assumed,  and  without  any  really  logical  basis  for 
the  assumption,  that  if  a  complex  atom  is  made  up  by  the  union  of  sim- 
ple atoms,  the  mass  of  the  complex  atom  must  be  exactly  equal  to  the 
masses  of  the  simple  atoms  entering  into  its  structure.  Rutherford, 
from  data  on  the  scattering  of  a-rays  in  passing  through  gold  leaf,  has 
calculated  an  upper  limit  for  the  radius  of  the  nucleus  of  a  gold  atom  as 
3.4  X  io~12  cm.  The  mass  of  this  relatively  heavy  atom  is,  according 
to  this  calculation,  practically  all  concentrated  in  this  extremely  small 
space,  which  is  so  small  that  it  could  no  longer  be  expected  that  the  mass 
of  such  a  nucleus,  if  complex,  would  be  equal  to  the  sum  of  the  masses 
of  its  component  parts.  In  fact,  since  the  electromagnetic  fields  of  the 
electrons  would  be  so  extremely  closely  intermingled  in  the  nucleus,  it 
would  seem  more  reasonable  to  suppose  that  the  mass  of  the  whole  would 
not  be  equal  to  the  sum  of  the  masses  of  its  parts.  The  deviation  from 
the  law  of  summation  cannot  be  calculated  on  a  theoretical  basis,  but  it 
can  easily  be  determined  from  the  atomic  weights,  if  the  assumption  is 
made  that  the  heavier  atoms  are  condensation  products  of  the  lightest 


35 

of  the  ordinary  elements,  that  is  of  hydrogen.  This  deviation  expressed 
in  terms  of  the  percentage  change,  is  what  has  already  been  determined, 
and  designated  as  the  packing  effect. 

Since  this  packing  effect  represents  a  decrease  in  weight^  the  first  prob- 
lem which  represents  itself  for  determination  is  the  sign  of  the  effect  which 
would  result  from  the  formation  of  the  positively  charged  nucleus  of  an 
atom  by  the  combining  of  positive  and  negative  electrons  into  some  form 
of  structure.  Richardson1  suggests  that  the  positive  nucleus  of  an  atom 
might  be  built  up  of  positive  electrons  alone  and  still  be  stable  if  the  law 
of  force  between  them  were 

+  a/r2  —  b/rpl  +  c/r**,  where  fr>pi>2. 

Here  the  first  term  gives  the  usual  law  of  force,  the  second  causes  the  elec- 
trons when  close  together  to  attract  each  other,  and  the  third  expresses 
the  repulsion  which  keeps  them  from  joining  together.  It  would,  how- 
ever, seem  more  simple  to  assume,  what  seems  much  more  probable, 
that  the  nucleus  is  held  together  by  the  attraction  of  positive  and  nega- 
tive electrons,  both  of  which  are  assumed  to  be  present  in  any  complex 
nucleus. 

Since,  even  when  the  mass  is  assumed  to  be  entirely  electromagnetic, 
there  still  remain  two  possibilities  even  for  the  simple  case  of  hydrogen, 
first,  that  the  hydrogen  nucleus  is  the  positive  electron,  and  second,  that 
it  may  be  complex,  it  has  seemed  best  to  choose  for  the  purpose  of  cal- 
culation the  simplest  system,  which  consists  of  one  positive  and  one  nega- 
tive electron.  The  problem  thus  presented  for  solution  is  the  determina- 
tion of  the  sign  and  the  magnitude  of  the  change  of  mass  which  results 
when  a  positive  and  a  negative  electron  are  brought  extremely  close  to- 
gether. 


eT  ~r  e, 

Lorentz2  speaks  of  this  problem,  but  does  not  solve  it  either  with  re- 
spect to  the  sign  or  the  magnitude  of  the  effect.  He  does  state,  however, 
that  if  the  electrons  were  to  be  brought  into  immediate  contact,  the  total 

1  "The  Electron  Theory  of  Matter,"  p.  582. 

2  H.  A.  Lorentz,  "The  Theory  of  Electrons,"  1909,  pp.  47  and  48. 


36 

energy  could  not  be  found  by  addition,  which  may  be  considered  as  equiv- 
alent to  the  statement  that  the  mass  of  a  system  made  up  in  this  way 
would  not  be  the  same  as  the  sum  of  the  masses  of  its  parts.  The  funda- 
mental equations  used  here  as  the  basis  of  the  calculation  which  follows, 
have  been  taken  from  the  work  of  Lorentz. 

The  value  of  e,  the  charge  on  the  electron,  may  be  defined  as 


///•*• 


where  p  is  the  volume  density  of  the  electricity,  and  dr  is  an  element  of 
volume.  For  the  purposes  of  the  first  part  of  the  calculation,  the  elec- 
tron may  be  considered  as  a  point  charge,  but  the  values  of  the  electro- 
magnetic mass  used  later  are  given  for  the  Lorentz  form  of  electron,  which 
takes  the  form  of  an  oblate  spheroid  when  in  motion. 

The  space  surrounding  an  electron  must  be  considered  as  different 
from  a  space  not  adjacent  to  an  electrical  charge.  If  a  charged  particle 
is  brought  into  this  space  it  is  acted  upon  by  a  force  which  varies  from 
point  to  point,  and  has  at  every  point  in  space  a  definite  value  and  direc- 
tion. This  force  is  designated  by  E,  and  is  a  vector  point  function.  If 
the  electron  is  in  motion  it  acts  as  an  electric  current  equal  to  eu,  where 
«  represents  its  velocity.  The  magnetic  force  due  to  this  motion  is  easily 
seen  to  be  a  function  of  the  current  equivalent  of  the  moving  electron, 
and  is  also  a  vector,  designated  by  H.  Then 

H  =  /  (E,  «,  </>) 

where  <f>  is  the  angle  between  E  and  the  direction  of  motion.  The  direc- 
tion of  H  is  perpendicular  to  the  direction  of  u  and  is  at  the  same  time  cir- 
cular. 

It  is  evident  that  the  total  energy  of  the  system  is  a  function  of  both 
the  electric  and  the  magnetic  intensities.  For  the  purposes  of  this  cal- 
culation the  mass  of  a  system  is  considered  as  electromagnetic,  and  hence 
as  a  function  of  the  energy  of  the  system.  Therefore  it  is  necessary  to 
use  some  function  of  both  E  and  H.  This  function  is  designated  by  G 
and  is  called  the  electromagnetic  momentum.  The  derivation  of  the  equa- 
tions for  G  has  been  given  by  Lorentz,  so  here  it  will  be  sufficient  to  de- 
fine it  as 

G  =  [E  H]/c 

where  [E  H]  means  the  vector  product  of  E  and  H,  and  c  is  the  velocity 
of  light.  From  the  expressions  obtained  for  G  it  is  easy  to  obtain  those 
which  represent  the  mass. 

In  the  treatment  which  follows,  only  the  longitudinal  electromagnetic 
mass  is  considered,  and  terms  containing  u  to  a  higher  power  than  the  first 
are  disregarded,  as  they  appear  to  be  unimportant.  The  following  gen- 
eral treatment,  in  which  Heaviside  units  are  used,  gives  an  outline  of  the 
method : 


37 

For  the  field  due  to  a  system  of  charges 
[EH] 


<7 

where  the  summation  S(#)  is  the  vector  product  of  each  i  with  each  ;'.     The 
first  summation  gives  the  electromagnetic  momentum  which  would  be 
due  to  the  particles  if  their  fields  did  not  overlap,  and  the  second  term, 
which  is  the  important  one  here,  gives  the  effect  of  the  overlapping  of  the 
fields.     This  may  be  called  the  "mutual  electromagnetic  momentum" 
.  and  designated  by  G. 
For  point  charges 

E    =  —z 


47rr2(i—  w2sin20i)J 
at  the  point  P*,  y>  z.     Let 

(i—  w2  sin2  ft)  =  ft2 
and 

(i—«»)  =  k*. 
The  transverse  component  of  E  due  to  the  two  particles  i  and  2  is 

E    -  —  /  s*n  fl*  ±  sin 
=  ^\^W-       f 

where  the  sign  is  positive  if  the  charges  have  the  same  sign,  and  negative 
if  they  are  of  opposite  sign.  As  only  the  longitudinal  component  of  the 
vector  G  is  desired,  only  the  transverse  component  of  E  is  needed. 

H  =  u/c  E  sin  <£ 

where  <£  =  the  angle  between  E  and  the  direction  of  u.  If  E/  is  used, 
0  =  90°.  Therefore 

H  =  u/c  (Ei  sin  0i  =*=  E2  sin  02) 


GL  =     -l      =  —  (Ei  sin  0i  =»=  E2  sin  02)(Ei  sin  0i  =*=  E2  sin  02). 


And 

_  2i/  f* 

G  =  =*=  -g  I  EiE2  sin  0i  sin  02  dr 

2U  k*e2     r  sin  0i  sin  02 


r2r2  j8, 
Now 


, 

( 


Neglect  all  of  the  terms  in  u2. 

dr  —  2irydydx. 
Then 


38 
which  is  obtained  by  making  use  of  the  symmetry  of  the  equation.     Or 


V(  '[(*  —  i)2  +  y*][(x  +  i) 


2irc2a  J 
where 

y*dxdy 


~  * 

where  «  =  y2. 


+  i) 
udu 


;     a  —  /?=(  —  4*)- 


T  ^ 

"  ' 


oo 


«  — «2       («  — /3)2V          ' 
° 


-  +  Z 
4        4 

i 

2 


/.G 


The  mass  represented  by  this  value  of  G  is 

Am  =  =*=  e^/^TTC^a. 
Now  the  longitudinal  mass,  mi  is 

mi  =  e2/6irczR, 
where  R  is  the  radius  of  the  electron.    By  division 

Am/mi  =  3R/2a, 
where  a  is  equal  to  one-half  the  distance  apart  of  the  electrons. 

In  the  application  of  this  last  equation,  R  must  be  taken  as  the  radius 
of  the  positive  electron,  since  it  is  assumed  that  it  is  the  seat  of  practically 


39 

all  of  t}ie  mass  of  the  atom.  For  a  decrease  of  mass  of  i%  in  this  simple 
case  the  distance  apart  of  the  positive  and  negative  electrons  would  be. 
according  to  the  equation,  300  times  the  radius  of  the  positive  electron. 
In  order  to  produce  a  decrease  of  mass  equal1  to  the  average  decrease  of 
weight  found  for  the  21  elements  given  in  Table  II,  or  OT77%,  the  dis- 
tance apart  of  the  two  electrons  as  calculated,  would  be  400  times  the 
radius  of  the  positive  electron.  This,  however,  does  not  give  the  resuls 
for  any  actual  case  which  is  known,  and  in  general  the  nucleus  of  an  atom 
must  be  more  complex  than  this.  In  a  more  complex  nucleus  it  is  possi- 
ble that  the  positive  and  negative  electrons  need  not  come  so  close  to- 
gether in  order  to  give  the  same  decrease  of  mass.  It  is  evident  that  the 
calculation  cannot  be  applied  to  any  special  atom  until  the  mass  of  the 
positive  electron  is  determined.  If,  as  Rutherford  seems  to  think  proba- 
ble, the  positive  nucleus  of  the  hydrogen  atom  is  the  positive  electron, 
then  the  most  probable  composition  of  the  helium  nucleus  would  be  four 
positive  electrons  to  two  which  are  negative,  and  it  would  not  seem  im- 
probable that  in  such  a  system  the  effect  upon  the  mass  of  the  positive 
electrons  might  be  greater  than  in  the  simpler  case  used  for  the  calcula- 
tion, which  would  mean  simply  that  the  positive  and  negative  electrons 
need  not  be  so  close  together  to  produce  the  same  effect  on  the  mass. 
Whether  this  is  true  or  not  could  not  be  determined  without  a  knowl- 
edge of  the  structure  of  the  helium  nucleus.  If,  as  Nicholson  as- 
sumes, the  hydrogen  nucleus  is  complex,  the  decrease  of  mass  in  the 
formation  of  one  helium  atom  from  four  of  hydrogen,  would  be  due  to 
the  closer  packing  of  the  positive  and  negative  electrons  in  the  helium 
nucleus. 

Earlier  in  the  paper  it  has  been  shown  that  the  fact  that  the  atomic 
weights  on  the  oxygen  basis  are  much  closer  to  whole  numbers  than  those 
on  the  hydrogen  basis,  is  explained  by  what  has  been  called  the  packing 
effect,  or  the  change  of  mass  involved  in  the  formation  of  heavier  atoms 
from  hydrogen.  The  ayerage  of  the  packing  effects  for  the  elements  con- 
sidered, is  0.77%.  This  is  also  the  value  of  this  effect  for  oxygen,  which 
happens  to  have  been  chosen  as  the  fundamental  element  in  the  deter- 
mination of  atomic  weights.  If  the  number  representing  atomic  weight 
of  hydrogen,  i  .0078,  is  decreased  by  this  percentage  amount,  it  becomes 
i  .0000,  which  is  the  fundamental  unit  in  atomic  weight  determinations. 
The  atomic  weights  of  the  twenty-five  fundamental  elements  listed  in 
Table  II,  are  found,  on  the  whole,  to  be  very  nearly  products  of  this  unit 
by  a  whole  number.  While  the  numerical  unit  of  measurement  does  not 
change,  the  actual  unit  of  mass,  the  mass  of  the  hydrogen  nucleus,  varies 

1  From  the  electromagnetic  theory  the  velocity  of  high  speed  electrons  also  exerts 
a  perceptible  influence  upon  the  mass,  but  the  magnitude  of  this  effect  has  not  as  yet 
been  determined  for  the  case  of  the  electrons  in  an  atom. 


40 

slightly  from  atom  to  atom,  and  this  variation  causes  the  slight  devia- 
tion of  the  atomic  weights  from  whole  numbers. 

The  opposite  of  the  system  here  proposed  would  be,  to  suppose  that 
the  values  of  the  atomic  weights  are  wholly  the  result  of  accident.  On 
this  basis  the  probability  that  the  atomic  weights  fall  as  close  to 
whole  numbers  as  they  do,  may  be  calculated.  In  such  calculations 
oxygen  is  omitted,  since  its  atomic  weight  is  fixed  as  a  whole  number, 
and  hydrogen  is  not  used,  since  its  atom  contains  only  one  hydrogen 
nucleus. 

The  first  calculation  made  was  that  of  the  probability  that  each  of  the 
atomic  weights  should  be  as  close  as  it  is  to  a  whole  number.  The  data 
used  are  those  of  Table  II.  The  chance  that  the  atomic  weight  of  nitro- 
gen should  entirely,  by  accident,  deviate  from  a  whole  number  by  only 
o.o i  of  a  unit  was  determined  by  dividing  the  unit  into  the  200  divisions 
corresponding  to  the  assumed  accuracy  (Landolt-Bornstein-Meyer- 
hoffer,  Tabellen)  of  0.005.  The  greatest  possible  deviation  would  then 
be  loo  divisions,  while  the  actual  deviation  of  o.oi  unit  corresponds 
to  2  divisions.  The  probability  is  then  one-fiftieth.  The  chance  that 
any  number  of  independent  events  should  all  happen  is  the  product  if  the 
separate  probabilities  of  their  each  happening.  The  probability  calcula- 
ted in  this  way  is  2  X  io~22,  or 

2 

10,000  billion  billion, 

which  indicates  that  there  is  practically  no  chance  that  the  atomic  weights 
are  entirely  the  result  of  accident. 

Another  probability,  which  seems  to  be  of  more  value  in  connection 
with  the  present  problem,  is  that  the  sum  of  the  deviations  shall  not  ex- 
ceed the  sum  actually  found.  This  is  of  the  form  known  as  De  Moivre's 
problem,  and  the  method  was  used  by  Laplace1  in  calculating  the  proba- 
bility that  the  sum  of  the  inclinations  of  the  orbits  of  the  ten  planets  to 
the  ecliptic  is  not  greater  than  the  value  foun/i  at  that  time,  0.914187 
of  a  right  angle.  The  result  obtained  was  i .  i  X  io~7.  The  problem  is 
stated  in  the  following  way :  An  urn  contains  n  +  i  balls  marked,  respec- 
tively, o,  i,  2,  3, n;  a  ball  is  drawn  and  replaced:  required  the  proba- 
bility that  after  i  drawings  the  sum  of  the  numbers  drawn  will  be  5.  This 
probability  is  the  coefficient  of  xs  in  the  expansion  of 


(n  +  i)' 
or  the  probability  P  is 

1  Laplace,  "Oeuvres  VII,  Theorie  Analytique  des  Probabilites,"  pp.  257-62. 


—  i)  K—  i+s  —  2  w—  2 


1.2      '     K—  I    \S-2jn  —  2     ' 

In  the  case  of  the  atomic  weights  P  gives  the  probability  that  the  sum 
of  the  deviations  from  whole  numbers  shall  equal  s,  which  is  not  what  is 
desired.     The  result  wanted  is  the  probability  that  the  sum  of  the  errors 
shall  be  equal  to  or  less  than  s,  or  the  summation  of  the  Ps  from  0  to  5. 
Now 


\i\s 
So  the  desired  probability,  P'  is: 

_  '-i    i     ri£+*     *  K  +*-»-i 

'  ' 


*(*—  0  K  +  s—  -2n  —  2  __  *(*—  -0(*—  -2)  |*'-i-s  —  3M—  -3  ) 

1.2        |e  |s  —  2M  —  2  1.2.3  II  !5  —  2n  —  3          '  ; 

In  solving  this  problem  all  of  the  first  twenty-seven  elements  have  been 
used  with  the  exception  of  hydrogen  and  oxygen,  and  these  should  be 
omitted  for  the  reasons  given  above.  The  errors  in  the  determined  values 
have  been  taken  as  they  are  given  in  Table  II.  The  atomic  weights  used 
in  the  calculation  are  as  follows: 

He  ..........  4.002  Mg  .........  24.32  Ca  ...........  40.07 

Li  ...........  6.94  Al  ..........  27.1  Sc  ...........  44.1 

Be.  ..........  9.1  Si  ...........  28.3  Ti  ...........  48.1 

B  ............  ii.  o  P  ...........  31.02  V  ............  51.0 

C  ...........  12.005  S  ............  32.06  Cr  ...........  52.0 

N  .....  '.  .....  14.01  Cl  ..........  35.46  Mn  ..........  54-93 

F  ............  19.00  A  ...........  39.88  Fe  ...........  55.84 

Ne  ..........  20.15  K  ...........  39-10  Co  ...........  58.97 

Na  ...........  22  .995 

The  average  probable  error  as  determined  from  Table  I  is  0.043  unit, 
which  is  equivalent  to  about  24  divisions  for  one  unit,  or  12  divisions 
for  half  a  unit,  which  is  the  maximum  possible  deviation  from  a  whole 
number.  Since  n  is  12,  n  +  i  is  taken  as  13.  The  sum  of  the  devia- 
tions from  whole  numbers  is  2.342,  which  is  equal  to  56  of  the  divisions 
determined  above,  or  s  =  56.  The  number  of  elements,  it  is  26.  The 
probability  calculated  on  this  basis  is  6.56  X  io~8,  or  approximately 


15,000,000 

It  has  been  assumed  in  this  paper  that  the  cause  of  the  deviations  of  neon, 
magnesium,  silicon,  and  chlorine,  which  are  exceptional  in  giving  positive 
deviations  from  the  atomic  weights  on  the  hydrogen  basis,  must  be  differ- 


42 

ent  from  that  which  gives  the  deviations  of  the  other  elements.  The  cause 
of  the  deviation  of  neon  has  been  explained,  but  for  the  others  it  is  un- 
known. In  the  calculations  of  the  probabilities  given  above  these  ele- 
ments have  been  included.  It  may  be  of  interest  to  note  that  if  these 
elements  had  been  excluded  the  probability  for  the  2 1  remaining  elements 
would  have  been  found  to  be  about 

i 

7  billion 

It  is  an  interesting  coincidence  that  the  probability  above  found  for  the 
27  lighter  elements  is  about  i  X  io~7,  while  the  probability  determined 
by  Laplace  that  the  sum  of  the  inclinations  of  the  ten  planets  then  known, 
to  the  ecliptic,  should  not  be  greater  than  the  sum  of  the  measured  values, 
is  almost  the  same,  or  i .  123  X  io~7.  In  the  second  paper  of  this  series 
it  will  be  shown  that  the  atomic  weights  not  only  approximate  whole 
numbers,  but  that  these  whole  numbers  are  in  addition  certain  numbers 
which  are  determined  by  a  special  system,  and  which  may  be  given  ac- 
curately by  an  equation  of  the  form 

W  =  2(n  +  n')  +  V,  +  [(—  I)*"1  X  y2]. 

The  probability  that  the  atomic  weights  should  come  so  close  to  these 
special  whole  numbers  is  much  less  than  that  calculated  above,  so  that 
the  words  of  Laplace  may  be  applied  to  the  system  presented  here,  as  well 
as  to  the  one  he  himself  gives.  That  the  atoms  are  built  up  of  units  of 
weight  very  close  to  one,  and  that  therefore  this  modified  form  of  Prout's 
hypothesis  holds,  "est  indiquee  avec  une  probabilite  bien  superieure  a 
celle  du  plus  grand  nombre  des  faits  historiques  sur  lesquels  on  ne  se 
permet  aucun  doute." 

The  accepted  atomic  weights  on  the  oxygen  basis  as  now  used  are  closer 
to  whole  numbers  than  those  given  by  Ostwald  in  I89O.1  Ostwald's 
numbers  are  all  larger  than  the  corresponding  whole  numbers,  so  the 
deviations  were  all  positive.  On  the  other  hand,  the  present  values  show 
both  positive  and  negative  deviations.  The  fact  that  the  small  change 
of  0.77%  from  the  oxygen  to  the  hydrogen  basis  eliminates  practically 
all  of  the  tendency  of  the  atomic  weights  to  be  near  whole  numbers, 
when  as  many  as  27  elements  are  considered  as  in  Table  II,  shows  that  the 
atomic  weight  of  oxygen  cannot  be  taken  as  very  different  from  16.00 
without  obscuring  this  relationship.  Thus  it  has  been  shown  that  the 
probability  that  the  atomic  weights  on  the  oxygen  basis  would  come 
entirely  by  accident  as  close  to  whole  numbers  as  they  do,  is  6.56  X  io~8, 
or  about 


15,000,000 
Allgemeine  Chemie,  i,  p.  126  (1890). 


43 

A  change  of  only  0.77%  from  the  oxygen  basis  causes  an  enormous 
increase  in  the  probability  that  the  atomic  weights  obtained  in  this  way 
could  be  as  close  to  whole  numbers  as  they  are,  entirely  by  accident. 
Thus  the  chance  that  the  sum  of  the  deviations  should  come  out  as  equal 
to,  or  less  than,  the  sum  actually  found,  is  o.  105,  or 

i 
10' 

As  has  been  seen,  there  are  27  atomic  weights  distributed  over  59 
units  of  atomic  weight.  The  greatest  common  divisor  of  the  whole  num- 
bers corresponding  to  the  atomic  weights  is  one.  The  atomic  weights 
are  therefore  such  that  numerically  they  seem  to  be  built  up  from  a  unit 
of  a  mass  of  one,  and  the  probability  results  seem  to  show  that  this  unit 
of  mass  must  be  very  close  to  i .  ooo,  expressed  to  three  decimal  places. 
On  the  other  hand,  this  unit  of  mass  must  be  somewhat  variable  to  give 
the  atomic  weights  as  they  are,  even  although  a  part  of  the  variation, 
in  some  cases,  may  be  due  to  the  inaccuracy  with  which  the  atomic  weights 
are  known.  This  leads  either  to  the  supposition  (i)  that  the  atoms  are  built 
up  of  some  unknown  elementary  substance,  of  an  atomic  weight  which 
is  slightly  variable,  but  is  on  the  average  extremely  close  to  i .  ooo,  and 
which  does  not  in  any  case  deviate  very  far  from  this  value,  or  to  the 
idea  (2)  which  is  presented  in  this  paper,  that  the  nucleus  of  a  known 
element  is  the  unit  of  structure.  The  atom  of  this  known  element  has  a 
mass  which  is  close  to  that  of  the  required  unit,  and  it  has  been  proved 
that  the  decrease  of  mass  involved  in  the  formation  of  a  complex  atom 
from  hydrogen  units  is  in  accord  with  the  electromagnetic  theory.  The 
adoption  of  the  first  hypothesis  would  involve  much  more  complicated 
relations.  It  would  necessitate  the  existence  of  another  elementary  sub- 
stance with  an  atomic  weight  close  to  that  of  hydrogen,  it  would  involve 
a  cause  for  the  increase  of  weight  in  the  formation  of  some  atoms,  and  a 
decrease  in  other  cases,  and  it  would  also  involve  the  existence  of  another 
unit  to  give  the  hydrogen  atom. 

In  the  second  paper,  which  follows,  still  more  evidence  in  favor  of  the 
theory  that  the  other  atoms  are  complex  atoms  built  up  from  hydrogen 
units  will  be  presented,  and  it  will  be  shown  that  there  is  also  an  important 
secondary  unit  of  structure. 

The  writer  wishes  to  thank  Professor  A.  C.  Lunn,  of  the  Department  of 
Mathematics,  for  outlining  for  him  the  mathematical  analysis  of  the 
•determination  of  the  packing  effect. 

Summary. 

i.  The  atomic  weights  of  the  first  27  elements,  beginning  with  helium, 
are  not  multiples  of  the  atomic  weight  of  hydrogen  by  a  whole  num- 
ber, as  they  would  be  if  Prout's  original  hypothesis  in  its  numerical  form 


44 

were  true.  This  may  be  expressed  by  the  statement  that  the  atomic 
weights  on  the  hydrogen  basis  are  not  whole  numbers.  However,  when 
these  atomic  weights  are  examined  critically  it  is  found  that  they  differ 
from  the  corresponding  whole  numbers  by  a  nearly  constant  percentage 
difference,  and  that  the  deviation  is  negative  in  sign,  with  an  average 
value  of  — o. 77%. 

2.  This  percentage  difference  has  been  called  the  packing  effect,  and  it 
represents  the  decrease  of  weight,  and  presumably  the  decrease  of  mass, 
which  must  take  place  if  the  other  atoms  are  complexes  built  up  from 
hydrogen  atoms.     The  regularity  in  this  effect  is  very  striking,  the  values 
for  a  number  of  the  lighter  atoms  being  as  follows :     He,  — o .  77 ;  B,  — o .  77 ;. 
C,  —0.77;  N,  —0.70;   O,  —0.77;  F,  —0.77;   and  Na,  —0.77%,  while 
the  average  value  for  the  first  27  elements  is  — 0.77%. 

3.  The  regularity  of  the  packing  effect  gives  an  explanation  of  the  well- 
known  fact  that  the  atomic  weights  on  the  oxygen  basis  are  very  close 
to  whole  numbers,  while  this  is  not  true  of  the  atomic  weights  on  the 
hydrogen  basis  except  in  the  case  of  the  lightest  elements  from  helium 
to  oxygen.     The  atomic  weight  of  hydrogen  on  the  oxygen  basis  is  i  .0078. 
If  this  were  decreased  by  the  value  of  the  packing  effect  of  0.77%,  it 
would  become  a  whole  number,  i .  ooo.     Then,  if  the  other  elements  are 
built  up  from  hydrogen  atoms  as  units,  all  of  the  atoms  which  are  formed 
with  a  packing  effect  of  — 0.77%,  must  have  whole  numbers  for  their 
atomic  weights ;  thus  the  atomic  weights  of  the  elements  listed  in  Section 
2,  above,  must  be  whole  numbers  in  six  of  the  seven  cases  listed,  He,  B, 
C,  O,  F,  and  Na.     The  fixing  of  any  one  of  these  six  atomic  weights  as 
whole  numbers  causes  the  other  five  to  be  whole  numbers  also.     Thus  the 
atomic  weights  referred  to  carbon  as  12.00  would  be  the  same  as  those 
referred  to  oxygen  as  1 6.00.     A  variation  of  the  atomic  weight  of  an  ele- 
ment on  the  oxygen  basis  from  a  whole  number  indicates  that  the  packing 
effect  for  that  element  does  not  have  the  average  value. 

4.  Recent  work  has  shown  that  the  nucleus  of  an  atom  must  be  ex- 
tremely minute.     Thus  Rutherford  gives  the  upper  limit  for  the  radius 
of  the  relatively  large  and  complex  gold  atom  as  3.4  X  io~12  cm.,  while 
Crehore,  who  proposes  another  theory  of  the  structure  of  the  atom,  con- 
siders that  none  of  the  electrons  have  orbits  of  a  greater  radius  than 
io~12  cm.     The  high  velocity  with  which  the  /3-particles  are  shot  out  in 
radioactive  transformations  has  been  considered  as  evidence  that  these 
electrons  must  come  from  much  closer  to  the  center  of  the  atom  than 
the  assumed  radius  of  the  atom.     It  therefore  seems  practically  certain 
that  the  "electrons  and  positively  charged  particles  which  make  up  the 
nucleus  of  a  complex  atom,   are   packed   exceedingly  closely  together. 
As  a  result  of  this  close  packing,  the  electromagnetic  fields  of  the  charged 
particles  must  overlap  to  a  considerable  extent,  which  would  mean  that 


45 

the  mass  of  the  atom  ought  not  to  be  equal  to  the  sum  of  the  masses  of  the 
individual  particles  from  which  it  is  built. 

5.  The  closeness  to  which  a  positive  and  a  negative  electron  would  have 
to  approach  to  give  a  decrease  of  mass  equal  to  0.77%,  or  the  average 
value  of  the  packing  effect,  is  found  by  calculation  to  be  to  a_distance  of  400 
times  the  radius  of  the  positive  electron.     This  case  does  not  correspond 
to  any  element  actually  known,  for  the  simplest  of  the  atoms  considered, 
helium,  may  be  supposed  to  have  a  nucleus  built  up  from  four  hydrogen 
nuclei  and  two  negative  electrons.     However,  the  magnitude  of  the  effect 
seems  to  be  of  the  order  which  would  be  expected. 

6.  The  probability  for  the  first  27  elements,  that  the  sum  of  the  deviations 
of  the  atomic  weights  (on  the  oxygen  basis  from  whole  numbers)  should 
by  accident  be  as  small  as  it  is,  is  found  to  be  one  chance  in  fifteen  million. 
On  the  other  hand,  a  change  of  only  0.77%  from  the  oxygen  basis  to 
that  of  hydrogen  gives  one  chance  in  ten  that  the  atomic  weights  should 
be  as  close  to  whole  numbers  as  they  are. 


Part  HI 

The  Structure  of  Complex  Atoms*    The  Hydrogen- 
Helium  System 


In  Part  II  it  has  been  shown  that  the  atomic  weight  relations  of 
the  elements  are  such  as  to  make  it  extremely  probable  that  the 
atoms  are  complex  structures  built  up  from  hydrogen  atoms.  It  therefore 
becomes  important  to  determine  in  what  way  the  hydrogen  atoms  unite 
together  to  make  up  the  complex.  Rutherford  proved  that  the  a-parti- 
cles  which  are  shot  out  in  the  disintegration  of  the  radioactive  elements, 
have  a  mass  of  four  units,1  and  that  they  give  ordinary  helium  gas  when 
they  escape  through  the  walls  of  a  thin  glass  capillary  tube  in  which  the 
emanation  is  stored.2  Fajans,3  Soddy,4  Russell,5  von  Hevesy,6  and  Fleck,7 
have  found  that,  when  a  radioactive  substance  ejects  an  a-particle,  the 
new  substance  has  different  properties,  and  a  different  valence  from  those 
of  the  parent  material.  The  change  is  such  that  the  new  element  lies 
two  places  to  the  left  in  the  periodic  table,  and  therefore  has  an  atomic 
number  which  is  two  less  than  before  the  alpha  disintegration.  It  has 
been  found  that  uranium,  for  example,  can  lose  eight  a-particles  in  eight 
steps,  and  change  into  a  form  of  lead.  From  this  it  is  seen  that  the  radio- 
active elements,  which  have  high  atomic  weights,  must,  at  least  in  part, 
be  built  up  of  a-particles,  and  therefore  of  helium  atoms,  with  this  differ- 
ence, that  while  the  a-particle  is  probably  present  as  a  whole  in  the  com- 
plex atom,  the  nonnuclear  electrons  of  the  helium  atom,  undoubtedly 
rearrange  themselves  in  the  complex  atom,  so  that  the  helium  atoms 
as  a  whole  do  not  preserve  their  identity. 

Now  that  it  has  been  proved  that  the  atoms  of  high  atomic  weight  are 
built  up,  in  part  at  least,  of  helium  atoms,  the  question  arises  as  to  whether 
the  same  relations  hold  for  the  lighter  atoms  which  have  not  been  found 
to  give  an  appreciable  alpha  disintegration.  If  they  do,  then  a  change 

1  Phil.  Mag.,   [6]  28,  552-72   (1914)- 

2  Rutherford  and  Soddy,  Phil  Mag.,  3,  582  (1902);  453  and  579  (1903);   Ramsay 
and  Soddy,  Nature,  p.  246  (1903);  Proc.  Roy.  Soc.,  72,  204  (1903);  73,  346  (1904); 
Curie  and  Dewar,   Compt.  rend.,   138,   190  (1904);  Debierne,  Ibid.,   141,  383   (1905); 
Rutherford,  Phil.  Mag.,  17,  281  (1909). 

:t  Physik.  Z.,  14,  131-6  (1913)- 

4  Chem.  News,  107,  97  (1913),  and  Jahrb.  Radioakt.,  10,  188  (1913). 

6  Ibid.,  107,  49  (1913)- 

6  Physik.  Z..  14,  49  (1914). 

7  Fleck,  Trans.  Chem.  Soc.,  103,  381  and  1052  (1913). 


47 

of  two  places  to  the  right  in  the  periodic  table,  which  is  more  accurately 
expressed  as  an  increase  of  two  in  the  atomic  number,  should  increase 
the  atomic  weight  by  the  weight  of  one  helium  atom,  or  by  the  number 
four.  Since  a  change  of  two  in  the  atomic  number  should  increase  the 
atomic  weight  by  four,  according  to  this  theory,  the  average  increase 
in  the  atomic  weight  per  atomic  number  should  be  two.  From  this  it 
might  be  expected  that  the  tenth  element  would  have  an  atomic  weight 
equal  to  20,  and  the  twentieth  element,  an  atomic  weight  of  40.  That 
this  is  actually  the  case  is  seen,  for  neon,  the  tenth  element  has  an  atomic 
weight  of  20,  and  calcium,  the  twentieth  element,  has  a  weight  of  40. 
In  order  to  investigate  the  question  more  in  detail,  a  start  may  be  made 
with  helium,  of  an  atomic  number  2  and  a  weight  of  4.  The  element  of 
an  atomic  number  four,  should  be  heavier  by  the  weight  4,  or  its  atomic 
weight  should  be  equal  to  eight.  Above  this  the  elements,  if  built  up  ac- 
cording to  this  helium  system  would  have  the  weights: 

Atomic  number.  Atomic  weight.  Group  number. 

6  124 

8  16  6 

10  20  o 

12  24  2 

14  28  4 

16  32  6 

where  each  step  is  made  by  adding  the  weight  of  one  helium  atom.  The 
equation  which  represents  the  idea  that  the  atomic  weights  of  the  lighter 
elements,  belonging  to  even  numbered  groups,  change  in  the  same  way 
as  the  elements  in  a  radioactive  series  (namely,  by  an  amount  equal  to  four 
for  a  change  of  two  groups  in  the  periodic  table),  is 

W    =    2W, 

where  W  is  the  atomic  weight  and  n  is  the  atomic  number. 

If  a  similar  system  is  supposed  to  hold  for  the  odd  numbered  elements, 
then  beginning  with  lithium  of  an  atomic  weight  seven,  and  an  atomic 
number  three,  the  atomic  weights  according  to  the  simple  helium  sys- 
tem would  be: 

Atomic  number.  Atomic  weight.  Group. 

3  7  I 

5  ii  3 

7  15  5 

9  19  7 

11  23  i 

13  27  3 

15  3i  5 

17  35  7 
19                                                        39  i 

It  is  thus  seen  that  for  the  odd  groups  as  well  as  the  even,  the  increase 


48 

in  the  atomic  weight  is  just  that  predicted  for  the  addition  of  one  helium 
atom  for  each  step  of  two  atomic  numbers.  The  even  and  odd  numbered 
elements  are  thus  seen  to  belong  to  two  different  series.  A  single  equa- 
tion for  both  of  these  series  may  be  easily  written  by  introducing  a  term 
which  disappears  when  n  is  even,  and  is  effective  when  n  is  odd.  If  W 
is  the  atomic  weight,1 

W    =    2H+    JI/2    +    [(—  I)""1    X    1/2]}. 

In  Table  I  the  atomic  weights  calculated  according   to  this  equation 
are  given  for  the  elements  up  to  and  including  cobalt. 

TABLE  I. — A  COMPARISON  OF  THE  CALCULATED  AND  THE  DETERMINED  VALUES  OF  THE 

ATOMIC  WEIGHTS.2 

Element.  n.  Calculated.  Detd.  Diff.  Probable  error  in  detn. 

He 2  4  4.0  O  O.OI 

Li 3                  7                  6.94  +0.06  0.05 

Be 4                  8                  9.1  — i.i     (=  iH)        0.05 

B 5                 ii  ii. o                   o  0.05 

C 6                 12  12.00                 o  0.005 

N 7                 15  14.01  +0.99  (=  iH)        0.005 

O ^8                 16  16.00                 o 

F 9                 19  19.0                   o  0.05 

Ne 10                 20  20.  o                   o                                ... 

Na ii                 23  23.00                 o  o.oi 

Mg 12                 24  24.32  — 0.32  0.03 

Al 13                 27  27.1  — o.i  o.i 

Si 14                28  28.3  — 0.3  o.i 

P 15                31  31.04  — 0.04  o.i 

S 16                32  32.07  — 0.7  o.oi 

Cl 17                 35  35.46  — 0.46  o.oi 

A 18                 36  39-88  — 3.88  (=  iHe)      0.02 

K 19                 39  39-10  — o.io  o.oi 

Ca 20  n>        40  40.07  — 0.07  0.07 

Sc 21  i         44 .  i  44 .  i  — o  .1  o.i 

Ti 22  2         48  48.1  — o.i  o.i 

V 23  2         51  51.0                  o  o.i 

Cr 24  2         52  52.0                  o  0.05 

Mn 25  2         55  54-93  +0.07  0.05 

Fe 26  2         56  55-84  +0.16  0.03 

Co 27  2         59  58.97  +0.03  0.02 

It  is  interesting  to  note  that  of  the  28  elements  in  this  table,  13,  or  very 

1  Although  it  was  not  known  to  the  writer  at  the  time  when  this  paper  was  written, 
it  was  found  on  looking  up  the  subject  that  Rydberg,  in  an  extremely  important  paper 
published  in  1896  (Z.  anorg.  Chem.,  14,  80)  found  from  a  study  of  atomic  weight  rela- 
tions that  the  elements  belong  to  two  series  corresponding  to  the  two  formulas  411  and 
4n-i,  where  n  is  a  whole  number.     Thus  from  an  empirical  basis  he  derived  the  same 
relationships  as  are  developed  in  this  paper  from  an  entirely  different  standpoint;  that 
is  by  the  applicat  on  of  the  relations  found  between  the  elements  in  a  single  radioactive 
series  to  the  e  ements  of  small  atomic  weight. 

2  For  the  final  equation  including  «'  see  section  3  of  the  summary. 


49 

nearly  half,  have  atomic  weights  which  are  divisible  by  4,  and  that  of  all 
of  the  possible  multiples  of  4,  only  two  are  missing,  i.  e.,  2  X  4  and  9X4. 
Seemingly  to  make  up  for  the  omission  of  the  9X4,  the  10  X  4  occurs 
twice.  This  may  be  represented  as  follows: 

1X4=  He  8X4  =  8 

2X4  =  missing,  but  represented  by        9X4  =  missing,  but  replaced  by 

(2X4)  +  !  10  X  4  =  A 

3X4  =  C  ioX4  =  Ca 

4X4  =  0  ii  X  4  =  Sc 

5  X  4  =  Ne  12  X  4  =  Ti 

6  X  4  =  Mg  13  X  4  =  Cr 

7  X  4  =  Si  14  X  4  =  Fe 

Of  the  atomic  weights  given  in  the  table  only  one  is  divisible  by  2, 
which  is  at  the  same  time  not  divisible  by  four.  Seven,  or  one-fourth  of 
the  atomic  weights,  are  divisible  by  3,  though  the  threes  are  not  evenly 
spaced  like  the  fours;  three  are  divisible  by  5,  and  two  of  these,  argon  and 
calcium,  have  the  same  atomic  weight.  Five  are  divisible  by  7,  and  two 
by  9,  and  every  possible  multiple  of  16  appears.  According  to  this  the 
most  important  numbers  are  4  and  3,  which  is  in  accord  with  the  equa- 
tion given  for  the  atomic  weights,  3  being  an  important  secondary  unit. 
<•  Of  the  twenty-six  elements  given  in  this  table,  it  is  found  that  the  equa- 
tion gives  the  atomic  weights  of  nine,  or  more  than  a  third,  with  no  differ- 
ence between  the  calculated  and  determined  values,  and  for  six  other 
elements  the  difference  is  practically  within  the  limits  of  error  of  the  de- 
terminations. For  the  three  elements,  Be  (+i .  i),  N  ( — 0.99),  and  argon 
( — 3.88),  the  differences  in  the  first  two  cases  are  practically  equal  to 
the  weight  of  a  hydrogen  atom,  and  for  argon  the  difference,  when  allow- 
ance is  made  for  a  possible  change  of  the  packing  effect,  is  the  weight  of  a 
helium  atom.  The  deviations  of  magnesium  (0.32),  silicon  (0.3),  and 
chlorine  (0.46),  are  somewhat  large,  the  largest  deviations  being  that  of 
chlorine,  which  is  equal  to  i  .3%  of  its  atomic  weight.  These  deviations 
are  also  exceptional  in  that  they  are  greater  on  the  basis  of  oxygen  as  16 
than  they  are  on  the  basis  of  hydrogen  as  i .  oo. 

If  these  six  cases  of  deviation,  three  of  which  can  be  explained  as  due 
to  a  deviation  in  the  number  of  hydrogen  or  helium  units,  are  neglected, 
it  is  found  that  for  the  other  twenty  elements  the  equation  gives  the 
atomic  weights  with  so  great  an  accuracy  that  the  average  deviation  is 
only  0.045  unit,  which  is  practically  equal  to  the  average  probable  error 
in  the  experimentally  determined  values  as  given  by  Landolt-Bornstein. 

It  has  been  seen  that  for  the  first  twenty  elements  the  average  increase 
in  weight  is  2 .  oo,  or  exactly  the  same  increase  as  is  found  for  the  uranium 
or  the  thorium  radioactive  series.  For  the  heavier  elements  the  increase 
is  somewhat  more  rapid.  The  increments  are  tabulated  in  Table  II. 


50 
TABLE  II. — THE  CHANGE  IN  THE  ATOMIC  WEIGHT  WITH  THE  ATOMIC  NUMBER. 

Change  of  atomic  number.        Final  element.  Atomic  wt.  Average  increment. 

o-io  Ne  20  2.0 

10-20  Ca  40.07  2.007 

20-30  Zn  65.37  2.53 

30-40  Zr  90.6  2.53 

40-50  Sn  119.0  2.84 

50-60  Nd  144.3  2.53 

60-70  Yb  172.0  2.52 

70-79  Au  197.2  2.80 

79-92  U  238.5  3.20 

The  table  shows  that  the  increment  2.00  occurs  twice,  and  2.52  four 
times  in  the  table.  The  increment  in  general  increases  with  the  atomic 
number. 

As  has  been  stated,  if  the  first  nine  elements  are  considered,  the  aver- 
age deviation  of  the  atomic  weights  (O  =  16)  from  whole  numbers  is 
only  0.019  unit,  which  is  an  extremely  small  deviation.  If  the  last 
ten  elements  in  Table  I  of  the  preceding  paper  are  taken,  it  is  found  that 
the  deviation,  though  much  larger,  is  still  small,  and  is  equal  to  0.075 
unit..  The  last  of  these  ten  elements  is  cobalt,  the  second  element  in 
the  eighth  group  for  the  first  occurrence  of  the  eighth  group  in  the  periodic 
table.  Table  III  shows  that  at  this  point  the  deviation  suddenly  jump's 
to  a  relatively  large  value,  being  0.32  for  nickel,  0.43  for  copper,  and  0.37 
for  zinc,  with  an  average  of  0.247  for  the  ten  elements  beginning  with 
nickel  and  ending  with  rubidium.  The  average  deviation  for  the  next 
ten  elements,  beginning  with  strontium  and  ending  with  cadmium,  is 
also  o. 247  unit,  for  the  ten  from  indium  to  cerium  it  is  o.  199,  and  for  the 
twelve  elements  from  tantalum  to  uranium,  it  is  0.260  unit.  However, 
the  value' of  Table  II,  as  it  stands,  is  very  slight  on  account  of  the  large 
probable  errors  in  many  of  the  atomic  weights.  This  can  be  remedied 
by  the  choice  of  only  such  elements  from  the  table  as  have  accurately 
determined  atomic  weights.  If  thirteen  elements  are  thus  chosen  as  fol- 
lows: nickel,  copper,  zinc,  arsenic,  bromine,  rubidium,  strontium,  rhodium, 
silver,  cadmium,  iodine,  caesium,  and  barium,  the  average  deviation  is 
0.248  unit,  while  the  theoretical  deviation  calculated  on  the  basis  that 
the  atomic  weights  show  no  tendency  to  be  near  whole  or  any  other  special 
numbers,  is  0.250  unit.  Therefore,  the  tendency  for  the  atomic  weights 
to  approximate  whole  numbers,  which  is  very  marked  for  the  elements 
from  helium  up  to  an  atomic  weight  of  59  (cobalt),  seems  to  altogether 
disappear  at  the  atomic  weight  59  (beginning  with  nickel)  and  is  not 
found  for  any  of  the  elements  which  have  an  atomic  weight  higher  than  this 
value. 

The  reason  for  this  abrupt  change  at  the  atomic  weight  59,  is  not  ap- 
parent. It  may  be  in  some  unknown  way  connected  with  the  first  ap- 


TABLE  III. — DEVIATIONS  OF  THE  ATOMIC  WEIGHTS  FROM  WHOLE  NUMBERS,  SHOWING 
THAT  FOR  THE  HEAVIER  ELEMENTS  THERE  IS  NO  TENDENCY  FOR  THESE  WEIGHTS 
TO  APPROXIMATE  WHOLE  NUMBERS. 

Heavier  elements.  Lighter  elements.1 


Diff.     Probable 

Diff.     Probable 

Diff. 

from 

error 

from 

error 

- 

from 

Ele- 

At. 

whole 

in 

Ele- 

At. 

whole 

in 

Ele- 

At. 

whole 

ment,           wt. 

no. 

at.  wt. 

ment 

wt. 

no. 

at.  wt. 

ment. 

wt. 

no. 

Ni.. 

..       58.68 

0.32 

0.02 

In. 

.  ..    114. 

8 

0.2 

0-5 

He. 

...     4  .  oo 

0.00 

Cu. 

•  •       63.57 

0-43 

0.05 

Sn. 

...    119. 

0 

0.0 

0-5 

Li- 

.  ..     6.94 

0.06 

Zn.. 

••       65.37 

0-37 

0.05 

Sb. 

.  .  .     I2O. 

2 

O.2 

0-3 

Be. 

...     9.1 

O.  IO 

Ga. 

60  o 

O.  IO 

O    => 

Te. 

127 

c 

O    "? 

O.2 

B 

no 

O.OO 

Ge. 

•  •        ^  V  •  V 

72     ^ 

o  .  50 

^  •  o 

o  s 

I... 

...     *  *•  /  . 
126. 

O 
Q2 

v  •  o 
0.08 

O   O^ 

c 

12    OO 

O  .  OO 

As.. 

I  •*•  •  o 
74.   96 

o  04 

v  •  O 
O   OS 

Xe. 

.     I^O. 

V 
2 

O.2 

\j  .  ^j^ 
O.2 

N 

I4.OI 

O.OI 

Se.. 

•  •          /  *r  •  7W 

7O    2 

*-/  •  ^^T" 

O.2O 

**  »  ^-'O 
O.  I 

Cs. 

•  •  •     •••  o^-'  • 
I*j 

81 

O    19 

O   OS 

F 

19   OO 

O.OO 

Br.. 

•  •        /  V  •  ~ 
••        79-92 

0.08 

O.  I 

Ba. 

.  .  .    *OA  • 
.  ..    137. 

37 

v-«  *y 

0.37 

\j  .  *-\} 
0.03 

Kr. 

.  .        82.92 

0.08 

O.I 

La. 

...    139- 

o 

0.0 

0.3 

Av. 

variation, 

0.024 

Rb. 

••        85.45 

0-45 

0.05 

Ce. 

...    140. 

25 

0.25 

O.I 

Na. 

...   23.00 

O.OO 

Av. 

variation, 

0.247 

Av. 

variation, 

0.199 

Al. 

.  .  .   27.10 

0.10 

P 

31  .02 

O.O2 

Sr.. 

87  63 

O    ^7 

o  O"* 

Ta. 

...    181. 

z 

o.  s 

i  .0 

s 

12  .07 

O.O7 

Y.. 

.    .            w  y    .  w^j 

.  .      89.0 

w*  «3  / 

0.0 

\j  .  *^o 

0.2 

W. 

.  ..    184. 

o 
0 

**  .  o 
0.0 

0.5 

V  .  W/ 

Zr.. 

90.6 

0.4 

O.2 

Os. 

.  ..    190. 

9 

O.I 

0.4 

Av. 

variation, 

0.047 

Cb. 

Q-I      C 

o  s 

Ir 

19^ 

i 

O.  I 

O.2 

Mo. 

•  •         yO  '  O 

.  .     96  .  o 

**  •  o 
0.0 

O.I 

Pt. 

.  ..     195. 

2 

0.2 

O.I 

Ar. 

...   39-88 

0.12 

Ru. 

.     IOI    7 

o.  i 

O.  I 

Au. 

•     197  • 

2 

O.  2 

O.  I 

K 

39-  IO 

O.  IO 

Rh. 

»%**  •  j 

...       102.9 

w  •  o 
O.I 

0.05 

Hg. 

*3Fff     ' 

.  .  .     200. 

6 

0.6 

0.4 

Ca. 

...   40.07 

0.07 

Pd. 

.   .       IO6.7 

0.3 

O.I 

Tl. 

.  .  .     204. 

0 

0.0 

0.2 

Ti. 

.  .  .   48.10 

0.10 

Ag; 

.   .       107.88 

O.  12 

O.O2 

Pb. 

.  .  .     207  . 

i 

O.  I 

O.  I 

V.. 

.  .  .   51.00 

O.OO 

Cd. 

..       II2.4 

0.4 

0.03 

Ra. 

.  .  .     226. 

4 

0.4 

0-3 

Cr. 

.  .  .   52.00 

0.00 



Th. 

.  .  .     232. 

4 

0.4 

0-5 

Mn 

•  •  •   54-93 

0.07 

Av. 

variation, 

0.247 

U.. 

...     238. 

5 

0.5 

0-5 

Fe. 

...   55.84 

o.  16 

Air 

Co. 

.  ..   58.97 

0.03 

/-\     ™(^r\ 

Av.  variation,    0.072 
1  For  a  complete  table  of  the  lighter  elements  see  Table  II  of  Part  II. 

pearance  at  this  point  of  new  series,  possibly  formed  by  disintegra- 
tion instead  of  aggregation;  to  a  change  in  the  effect  of  packing,  or, 
if  atoms  exist  which  are  lighter  than  hydrogen,  it  might  possibly  be 
due  to  their  inclusion.  If  the  first  suggestion  is  considered,  it  is  found 
that  when  the  elements  of  high  atomic  weight  are  reached  several  series 
are  known  to  exist.  Thus  the  isotopes  of  lead,  lead  from  radium  and 
radium  B  differ  in  atomic  weight  by  eight  units,  the  isotopes  radium  F 
and  radium  A  differ  by  the  same  amount,  and  radio-thorium  and  uranium 
Xi  differ  by  six  units.  If  the  members  of  the  actinium  series  could  be 
included,  some  of  these  differences  in  the  weights  of  one  species  of  atom 
would  be  made  even  larger.  Where  such  differences  exist  in  the  weights 
of  the  different  atoms  having  a  single  atomic  number,  it  cannot  be  ex- 


52 

pected  that  any  very  simple  relations  can  be  found  to  exist  for  atoms 
of  a  high  atomic  weight,  except  where  it  is  possible  to  compare  the  weights 
of  the  members  of  a  single  series,  such  as  the  uranium-radium,  the  thorium, 
or  the  actinium  radioactive  series. 

It  is  quite  possible  that  these  differences  of  series  go  downward  in 
the  periodic  system  to  relatively  low  atomic  weights.  Thus  Aston  claims 
to  have  separated  neon,  with  an  atomic  weight  20.2,  into  neon  and  meta- 
neon,  the  atomic  weights  for  which  have  been  found  by  Thomson  to  be 
20  and  22.  so  that  the  deviation  of  neon  from  the  law  of  the  approximate 
whole  number  by  the  amount  +0.2  is  probably  only  an  apparent  one. 
It  is  of  interest  that  the  difference  between  the  atomic  weights  of  neon 
and  meta-neon,  as  found  by  Thomson,  is  two,  which  is  the  same  as  the 
average  increment  in  the  weights  of  the  lighter  elements,  and  is  equal  to 
the  average  difference  between  the  weights  of  isotopes  in  the  radioactive 
series.  This  average  difference  has  been  supposed  to  be  also  the  actual 
difference  between  any  two  adjacent  isotopes  as  listed  below  under  any 
single  atomic  number: 

Atomic  number. 

82.  Lead  from  Ra,  Lead  from  Th,  Ra  D,  Th  B,  Ra  B. 

83.  Bi,  Ra  E,  Th  C,  Ra  C. 

84.  Ra  F,  Th  C,  Ra  C,  Th  A,  Ra  A. 
86.  Th  Em,  Ra  Em  (Nt). 

88.         Th  X,  Ra,  Ms  Th. 
90.         Ra  Th,  Io,  Th,  UX,. 

However,  these  assumed  differences  of  two  have  depended  upon  the 
fact  that  the  atomic  weights  used  for  uranium  and  thorium  have  been 
238.5  and  232.4,  or  a  difference  of  practically  4  plus  2.  The  latest  de- 
termination of  the  atomic  weight  of  uranium  by  Honigschmidt1  gives 
a  value  of  238. 1 8,  which  would  not  accord  with  this  relationship  for  the 
individual  differences.  The  difference  between  two  isotopes  belonging 
to  a  single  radioactive  series  is,  however,  not  affected  by  this  result,  and 
may  still  be  assumed  as  four.  However,  in  radioactive  changes  where  a 
helium  atom  is  lost,  the  new  atom  which  is  formed  is  not  exactly  four 
units  lighter  than  the  parent  atom,  since  the  packing  effect  varies  with  the 
change.  How  this  effect  varies  in  these  heavy  atoms  cannot  be  told  from 
the  data  now  available,  since  the  accuracy  of  the  atomic  weight  determina- 
tions is  not  sufficient  for  this  purpose,  but  the  variation  may  be  calculated 
approximately  from  the  heat  evolved  in  all  cases  where  the  heat  change  can 
be  determined.  It  is  of  course  self-evident  that  for  deductions  in  regard 
to  such  atomic  weight  relations,  the  percentage  accuracy  must  be  much 
greater  than  is  necessary  for  the  study  of  the  lighter  elements.  The  differ- 
ence between  Honigschmidt's  values  for  uranium  and  for  radium2  (at. 

1  Z.  Electrochem.,  20,  449  (1914). 

2  Sitzungsb.  kais.  Akad.  Wien.,  121,  Abt.  II A,  1973  (1912);  Monatsh.,  34,  283  (1913). 


53 


wt.  =  225.97)  is  12.21,  or  0.21  more  than  the  weight  of  three  helium 
atoms. 

Now  that  certain  elements  have  been  found  to  exist  in  isotopic  forms, 
it  becomes  apparent  that  still  other  elements  may  do  the  same  in  cases 
which  have  not  been  recognized,  so  that  in  dealing  with  any-single  species 
of  element  it  is  uncertain  whether  this  is  an  individual  with  respect  to 
its  atomic  weight.  The  great  regularity  with  which  the  elements  follow 
the  relationships  given  in  these  papers,  up  to  an  atomic  weight  of  59, 
suggests  that  with  the  exception  of  the  cases  of  neon,  silicon,  magnesium, 
and  chlorine,  isotopes  probably  do  not  exist  to  any  large  extent  for  any 
of  these  elements,  if  they  exist  at  all.  There  is  still  another  possibility 
which  suggests  itself,  and  that  is  that  the  different  atoms  of  a  single 
atomic  species  differ  in  weight  among  themselves,  and  that  the  atomic  weights 
as  found  are  simply  statistical  averages.  If  this  were  true,  the  constancy 
of  the  results  obtained  in  atomic  weight  determinations  which  after  all 
is  not  of  an  extremely  high  order,  would  be  due  to  the  fact  that  in  a  single 
determination  such  an  enormous  number  of  atoms  is  used.  For  example, 
if  in  one  determination  the  weight  of  silver  chloride  obtained  were  7 . 16  g., 
the  number  of  chlorine  or  silver  atoms  in  the  precipitate  would  be  3  X 
io22,  or  thirty  thousand  billion  billion.  The  statement  of  the  above 
idea  is  not  meant  to  be  understood  as  an  advocacy  of  such  a  theory,  but 
only  to  point  out  the  possibility  that  such  might  be  the  case. 

TABLE  IV. — A  SYMBOLICAL  REPRESENTATION  OF  THE  ATOMIC  WEIGHTS  OF  THE  ELE- 
MENTS IN  THE  FIRST  THREE  SERIES  OF  THE  PERIODIC  TABLE. 

H  =  i  .0078. 


0.       1         1.        |        2. 

3.        j      4. 

5. 

6..     |        7. 

8. 

Ser.  2. 

Theor. 
Det.. 

He 
He 

4.00 
4.00 

Li             Be 

He  +  Hi  2He  +  H 

7  .00        9.0 
6.94       9-1 

II.  0 
II.  0 

3He 
12.00 
12  .OO 

N 

14.00 

14.01 

O 

4He 

16.00 
16.00 

F 

4He  +  H» 

I9.OO 
19.00 

Ser.  3. 
Theor. 
Det  .. 

Ne 
5  He 

20.0 
2O.  O 

Na 

23.00 
23.00 

Mg 
6He 

24.00 
24.32 

Al 
6He  +  Hs 

27.0 
27.1 

Si 
7He 

28.0 
28.3 

P 

31-00 
31.02 

S 
8He 

32.00 
32.07 

Cl 
8He  +  Hi 

35-00 
35.46 

Ser.  4. 

Theor. 
Det.. 

A 
lOHe 

40.0 
39-9 

K 

9He  +  H» 

39-00 
39-10 

Ca 
lOHe 

40.00 
40.07 

Sc 
11  He 

44-0 
44.1 

Ti 
12He 

48.0 
48.1 

V 
12He 

51-0 
51-0 

Cr 
13He 

52.0 
52.0 

Mn 
13He 
+  Hi 

55-00 
54-93 

Fe 
14He 

56.00 
55.84 

Co 

14He 

+  HI 
59-00 
58.97 

Increment  from  Series  2 
Increment  from  Series  3 
Increment  from  Series  4 


to  Series  3  =  4-He 

to  Series  4  =  5  He  UHe  for  K  and  Ca) 

to  Series  5  =  6He 


Table  IV  gives  Series  2,  3  and  4  of  the  periodic  system,  built  up  by  add- 
ing the  weight  of  one  helium  atom  for  each  change  of  two  places  to  the 
right,  and  by  adding  enough  multiples  of  the  weight  of  a  hydrogen  atom 
to  make  up  the  atomic  weight.  In  order  to  make  the  relationship  ap- 


54 

parent  a  symbolical  representation  has  been  used,  He  being  taken  to 
stand  for  the  weight  4,  and  H  for  the  weight  i .  oo.  Built  up  in  this  way, 
the  atomic  weights  of  all  of  the  members  of  the  even  numbered  groups 
(with  the  exception  of  beryllium)  may  be  represented  by  a  whole  number 
of  symbols  He,  while  all  of  the  atomic  weights  in  the  odd  groups  may  be 
represented  by  3H  plus  a  whole  number  of  symbols  He. 

In  the  fourth,  or  argon  series,  the  atomic  weights  begin  to  increase  more 
rapidly  than  in  the  second  and  third  series.  This  effect  is  first  seen  in 
the  case  of  argon,  which  with  a  calculated  atomic  weight  of  36,  has  in- 
stead a  weight  of  practically  forty,  or  too  much  by  the  weight  of  one  helium 
atom.  This  effect  dies  out  in  potassium  and  calcium,  and  then  appears 
again  in  scandium,  titanium  and  the  other  members  of  this  series.  It 
becomes  apparent  in  another  way  on  studying  the  increment  of  weight 
in  passing  from  a  member  of  one  series  to  the  corresponding  member 
of  the  series  below  it.  Thus  the  second  member  in  each  group  is  ob- 
tained from  the  first  by  adding  4He.  In  going  from  the  second  to  the 
third  member  of  the  group  the  increase  is  the  same  (4.He)  to  give  potas- 
sium or  calcium,  but  is  5He  to  give  argon,  titanium,  vanadium,  chromium, 
and  manganese.1  This  in  a  sense  explains  how  the  atomic  weight  of 
argon  comes  to  be  greater  than  that  of  potassium,  and  practically  equal 
to  that  of  calcium.  In  going  from  the  third  to  the  fourth  member  of 
each  group,  it  is  necessary  to  add  6He,  but  the  increase  in  this  case  seems 
to  be  due  to  the  interposition  of  the  eighth  group  elements,  iron,  cobalt, 
and  nickel. 

While  both  the  law  of  the  approximate  whole  number,  and  the  hydro- 
gen-helium system  here  presented,  become  suddenly  much  less  accurate 
beginning  with  the  element  nickel,  this  does  not  necessarily  mean  that 
the  hydrogen-helium  system  breaks  down  at  this  point,  since  there  are 
several  possible  causes,  already  mentioned,  which  may  account  for  the 
sudden  increase  in  the  deviations.  The  eighth  group  fills  the  position  of  a 
transition  group  between  the  seventh  group  and  the  first,  which  shows 
that  it  fills  exactly  the  place  of  the  zero  group  in  the  other  series.  The 
first  member  of  the  eighth  group  tried  thus  has.  an  even  number  as  its 
atomic  number.  The  second  member  has  an  odd,  and  the  third  an  even 
number,  which  gives  to  the  first  group  an  odd  atomic  number.  This  is* 
entirely  in  accord  with  the  system,  which  would  fail  at  this  point  if 
there  had  been  two  instead  of  three  members  in  each  position  in  the 
eighth  group. 

According  to  the  rule  that  the  atomic  weights  of  the  elements  increase 

alternately  by  3  and  by  i,  then  since  iron  has  a  weight  of  56,  that  of  cobalt 

should  be  59  (detd.  =  58.97),  nickel  should  be  60  (detd.  =  58.68),  and 

1  In  comparison  with  the  other  members  of  the  same  series  it  is  potassium  and; 

calcium  rather  than  argon,  which  are  exceptional. 


55 

copper  63  (detd.  =  63.57).  The  first  large  negative  deviation  among 
the  elements  of  even  atomic  numbers,  of  any  of  the  actual  atomic  weights 
from  the  theoretical  value,  is  thus  found  for  the  element  nickel.  Now  it 
has  been  found  that  if  it  is  studied  from  the  standpoint  of  its  behavior 
toward  X-rays,  nickel  behaves  as  an  element  of  a  constftefably  higher 
atomic  weight  than  the  determined  value.  The  wave  lengths  of  the 
strong  K  radiations  as  found  by  Moseley  are  proportional  to  the  recipro- 
cals of  the  squares  of  the  atomic  weights.  If  cobalt  is  taken  as  a  stand- 
ard of  reference  (the  square  of  the  atomic  weight  and  wave  length  being 
taken  as  100  for  this  element),  the  values,  part  of  which  were  calculated  by 
Kaye, x  come  out  as  follows : 2 

Al.  Si.  Cl.  K.       Ca.        Ti.        V.        Cr.       Mn. 

(Atomic  weight) 21.1       23.0       36.1       44       46       66       75       78       86 

i /Wave  length 21.5       25.2       37.8       47       53       65       72       78       85 

Fe.         Go.         Ni.          Cu.         Zn.         Rh.          Pd.         Ag. 

(Atomic  weight) 90       100         99       116       123       304       328       334 

i /Wave  length 92       100       108       116       124       298       314       321 

The  atomic  weight  of  nickel,  if  calculated  from  the  value  108  as  given 
in  this  table,  comes  out  as  about  61.2,  while  the  other  elements  from  titan- 
ium up  to  and  including  rhodium,  give  a  very  close  agreement.  The 
principle  as  given  above  is  derived  from  Whiddington's  result  that  the 
energy  of  a  characteristic  X-ray  is  roughly  proportional  to  the  atomic 
weight,  and  from  the  quantum  theory  of  radiation,  according  to  which 
the  energy  of  a  radiation  is  inversely  proportional  to  its  wave  length. 

A  study  of  the  packing  effects,  as  given  in  Table  II  of  the  preceding 
paper,  shows  that  where  an  atom  is  built  up  entirely  of  helium  atoms, 
then,  on  the  average,  the  decrease  in  mass  is  practically  due  entirely 
to  the  primary  formation  of  the  helium  atoms,  and  not  at  all  to  the  aggre- 
gation of  these  into  atoms  which  are  heavier.  From  this  point  of  view 
an  atom  composed  entirely  of  helium  units  would  have  extreme  insta- 
bility in  so  far  as  its  disintegration  into  helium  units,  in  comparison  with 
its  instability  with  reference  to  a  hydrogen  decomposition.  Such  an  atom 
in  a  radioactive  transformation  should  lose  a-particles  much  more  readily 
than  hydrogen  nuclei,  in  fact,  if  it  is  remembered  that  the  alpha  decom- 
position is  itself  not  complete  in  any  case,  it  will  be  seen  that  it  is  doubt- 
ful if  such  an  atom  would  ever  give  a  detectable  hydrogen  disintegration. 

If  the  atoms  are  built  up  entirely  according  to  the  special  system  pre- 
sented in  Table  IV,  according  to  which  the  members  of  even  numbered 
groups  are  in  general  aggregates  of  helium  alone,  then  since  all  of  the 
radioactive  elements  which  are  now  known  to  give  a  simple  alpha  decom- 

1  "X-Rays,"  200. 

2  This  table  could  be  extended  by  including  the  values  of  the  nuclear  charge,  when 
it  would  be  seen  that  the  wave  lengths  seem  to  be  determined  by  the  nuclear  charge  as 
found  by  Moseley,  rather  than  by  the  atomic  weight. 


56 

position  (that  is  without  an  accompanying  beta  change)  belong  to  even 
numbered  groups,  they  could  not  be  expected  to  give  hydrogen  upon 
disintegration.  Thus  one  of  the  chief  objections  to  the  theory  that  the 
atoms  are  hydrogen  complexes,  which  is  based  on  the  fact  that  up  to  the 
present  time  no  hydrogen  has  been  detected  as  the  product  of  any  radio- 
active change,  is  seen  to  be  not  contrary  to,  but  rather  in  accord  with, 
the  theory  as  presented  in  these  papers.  The  exceptional  case  of  beryl- 
lium shows,  however,  that  even  numbers  of  even  numbered  groups  some- 
times contain  a  hydrogen  nucleus  which  was  not  contained  in  one  of  the 
helium  nuclei  from  which  the  atom  was  built,  so  that  there  still  remains 
the  possibility,  though  the  probability  seems  small,  that  hydrogen  nuclei 
might  be  liberated  from  atoms  belonging  to  these  groups.  There  is  no 
evidence  that  the  particular  system  presented  in  Table  IV  holds  exactly 
for  the  atoms  of  high  atomic  weight,  but  the  general  form  of  the  system 
indicates  at  least  that  the  atoms  contain  more  helium  than  independent 
hydrogen  units,  and  this  seems  in  accord  with  the  fact  that  uranium 
loses  a-particles  in  eight  steps,  and  is  changed  into  a  form  of  lead,  with- 
out any  apparent  loss  of.  a  hydrogen  nucleus. 

The  stability  with  which  the  hydrogen  nuclei  which  are  not  contained 
in  helium  groups,  but  which  generally  occur  in  threes  (Hs  in  Table  II), 
are  built  into  the  complex  atoms,  is  not  indicated  with  any  degree  of 
accuracy,  but  in  the  case  of  lithium  it  seems  to  be  great,  for  lithium  shows 
the  extremely  large  packing  effect  equal  to  1.57%,  which  might  seem 
doubtful  but  for  the  care  taken  by  Richards  and  Willard1  in  the  deter- 
mination of  this  atomic  weight. 

The  hydrogen-helium  system  here  presented  is  entirely  in  accord  with, 
but  independent  of,  the  astronomical  theory  that  the  order  in  which 
the  elements  appear  in  the  stars  is  first  nebulium,  hydrogen  and  helium, 
then  such  of  the  lighter  elements  as  calcium,  magnesium,  oxygen,  and 
nitrogen,  and  finally  iron,  and  the  other  heavy  metals,  although  in  the 
present  system  it  has  not  been  found  necessary  to  include  nebulium. 
Some  of  the  nebulae  give  bright  line  spectra  of  nebulium,  hydrogen  and 
helium,  such  Orion  stars  as  those  of  the  Trapezium  give  lines  for  hydrogen 
and  helium,  while  those  that  are  more  developed  show  magnesium,  silicon, 
oxygen  and  nitrogen,  and  some  of  the  other  low  atomic  weight  elements 
in  addition.  Bluish  white  stars  such  as  Sirius  give  narrow  and  faint 
lines  for  iron,  sodium,  and  magnesium,  and  the  solar  stars  give  much 
weaker  hydrogen  spectrum,  and  many  more  and  stronger  lines  for  iron 
and  the,  heavy  metals.  The  astronomical  theory  that  the  heavier  ele- 
ments are  thus  formed  from  those  of  smaller  atomic  weight  is  of  extreme 
interest,  but  the  evidence  for  it  is  somewhat  uncertain,  since  it  is  possi- 
ble that  it  is  the  difference  in  the  density  of  the  different  elements  which 
1  Richards  and  Willard,  /.  Am.  Chem.  Sac.,  32,  4  (1910). 


57 

is  the  effective  factor  in  causing  the  spectra  to  appear  in  the  order  in  which 
they  are  found  to  occur.  The  relative  brightness  of  the  different  lines, 
also  varies  greatly,  such  lines  as  the  calcium  H  and  K  lines  being  extremely 
strong,  and  this  also  interferes  with  the  determination  of  the  order  of  the 
appearance  of  the  elements  in  the  stars.  On  the  other  hand, _the  evidence 
presented  in  these  papers,  which  seems  to  show  that  the  elements  are  atomic 
compounds  of  hydrogen  and  helium,  appears  to  give  some  support  to  the 
theory  of  the  evolution  of  the  heavier  atoms  from  those  which  are  lighter. 
The  evidence  for  the  hydrogen-helium  system  is,  however,  very  much 
stronger  and  more  complete  than  that  for  the  evolution  of  the  elements 
in  the  stars. 

Summary. 

1.  The    fundamental    idea    of    this    paper    on    atomic    structure,    is 
to    show    that    the    system    which   has     been    found    to    apply    to    the 
atomic  weight  and  valence  relations  of  the  members  of  each  of  the  radio- 
active series,   also  holds  true  for  the  lighter  atoms.     In  a  radioactive 
series  it  is  found  that  a  loss  of  an  a-particle  with  a  mass  of  four  decreases 
the  valence  by  two,  and  thus  shifts  the  element  two  groups  to  the  left  in 
the  periodic  table,  and  decreases  the  atomic  number  by  two.     If  this  is 
true  for  the  lighter  elements,  beginning  with  Helium,  then  the  addition 
of  the  weight  of  a  helium  atom  for  each  increase  of  two  in  the  atomic  num- 
ber ought  to  give  the  atomic  weights  of  the  elements  belonging  to  the 
even   numbered   groups.     The   atomic   weights   found   by   this   method 
are  the  same  on  the  whole  as  the  determined  values,  which  shows  that 
the  theory  accords  with  the  facts. 

2.  The  lithium  atom,  which  is  the  first  atom  in  the  odd  numbered 
group,  is  heavier  than  the  helium  atom  by  the  weight  of  three  hydrogen 
atoms.     It  would  be  very  remarkable  if  the  atoms  of  odd  atomic  number 
follow  the  same  rule  as  those  of  even  atomic  number,  but  that  they  do 
is  indicated  by  Table  IV,  which  shows  that  for  the  odd  numbered  groups 
as  well,  each  increase  of  two  in  the  atomic  number  results  in  an  increase 
of  four  in  the  atomic  weight. 

3.  The  atomic  weights  of  the  lighter  elements  are  given  with  consid- 
erable accuracy  by  the  equation 

W  =  2W  +  (1/2  +  1/2  (—  I)""1), 

where  W  is  the  atomic  weight  and  n  the  atomic  number.  In  the  case  of 
the  heavier  elements  another  term  enters,  so  that  the  more  general  equa- 
tion may  be  given: 

W  =  2  (n  +  n')  +  [1/2  +.1/2  (-i)"-1] 

4.  Of  the  27  elements  from  helium  to  cobalt,   13,  or  nearly  one-half, 
have  atomic  weights  divisible  by  four,   and   these  elements  in  general 
belong  to  even  numbered  groups  in  the  periodic  table.     Of  all  the  possi- 


58 

ble  multiples  of  four  only  two  are  missing,  i.  e.,  2  X  4  and  9X4,  and 
seemingly  to  make  up  for  the  omission  of  the  9X4,  the  10  X  4  occurs 
twice.  An  explanation  of  the  omission  of  the  2X4  and  its  occurrence 
as  (2  X  4)  +  i  will  be  given  in  a  later  paper. 

5.  If  the  atomic  weights  increase  by  the  weight  of  one  helium  atom 
for  an  increase  of  two  in  the  atomic  number,  the  average  increase  in  the 
atomic  weight  per  atomic  number  should  be  2.     That  this  is  in  accord 
with  the  facts  is  shown,  for  neon  with  an  atomic  number  10  has  an  atomic 
weight  of  10  X  2  or  20,  and  calcium,  with  an  atomic  number  20,  has  an 
atomic  weight  equal  to  20  X  2  or  40. 

6.  According  to  Part  II,    the    magnitude    of   the   packing    effect   for 
helium  is  0.77%,  which  is   the   same   as   the   average   of   the   packing 
effects  for  the  first  27  elements,  so  that  if  a  more  complex  atom  is  built 
of  helium  groups  alone,  then  in  general  nearly  all  of  the  packing  effect 
is  due  to  the  primary  formation  of  the  helium  nucleus  from  four  hydrogen 
nuclei  and  two  negative  electrons,  and  almost  no  packing  effect  results 
from  the  aggregation  of  these  helium  nuclei  into  more    complex    atoms. 
On  this  view  the  helium  nuclei  must  be  very  greatly  more  stable  than  the 
nuclei  of  the  more  complex  atoms  which  they  form,  so  that  such  an  atom, 
made  up  entirely  from  helium  units,  should  give  helium  and  not  hydrogen: 
by  its  primary  decomposition.     This  is  in  accord  with  the  behavior  of 
the  radioactive  elements  when  they  disintegrate.     It  is  of  interest  to- 
note  that  the  members  of  the  radioactive  series  which  are  now  known 
to  give  helium  on  decomposition,  belong  to  the  even  numbered  groups 
on  the  periodic  table,  and  therefore  to  those  groups  which  are  shown  in- 
Table  IV,  as  helium  aggregates  alone.     That  these  heavy  atoms  must 
contain  a  considerable  number  of  helium  units  is  shown  by  the  fact  that 
uranium  changes  into  lead  by  eight  steps  in  which  it  loses  a-particles. 

7.  The  hydrogen-helium  system  gives  an  explanation  of  the  fact  that 
argon  has  an  atomic  weight  of  40,  which  is  higher  than  that  of  potassium, 
which  has  an  atomic  number  higher  by  i.     A  study  of  Table  IV  makes 
the  reason  apparent,  and  shows  that  in  comparison  with  other  members 
of  Series  4  in  the  periodic  table,  it  is  potassium  and  calcium,  and  not 
argon,    which    are    exceptional.     In    comparison    with    the   members   of 
Series  3,  and  potassium  and  calcium,  it  is  of  course  the  argon  which  is 
exceptional.     As  the  atoms  grow  heavier  there  is  a  tendency  to  take  on 
helium  (or  perhaps  hydrogen)  groups  more  rapidly  than  is  the  rule  in  the 
case  of  the  lighter  elements. 

The  writer  wishes  to  express  his  sincere  thanks  to  Dr.  W.  D.  Harkins, 
under  whom  this  investigation  has  been  carried  out,  for  his  continued  in- 
terest in  the  work,  and  for  his  many  suggestions. 

CHICAGO.  ILL. 


This  book  is  DUE  on  the  last  date  stamped  below. 

Fine  schedule:  25  cents  on  first  day  overdue 

50  cents  on  fourth  day  overdue 
One  dollar. on  seventh  day  overdue. 


KU/ULU 


072 -10 


LD  21-100m-12,'46(A2012sl6)4120 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 

mmmmmm 

U.  C.  BERKELEY  LIBRARIES 


COL13L2tll 


